If p is prime prove that p^1/2 (root p) is irrational. Generalize the proof that sqrt 2 is irrational. You can find several proofs here: http://www.cut-the-knot.org/proofs/sq_root.shtml You should be able to apply the proof to all square roots of prime

13,969 results
  1. math

    1. Which of the following numbers is a rational? A. 4/5 B. square root of 27 C. 4.02002000200002... D. Square root of 31 2. Which type of number is shown below? 0.313311333111... A. repeating decimal B. rational C. irrational D. terminating decimal 3.

  2. Math ~CHECK MY ANSWER~

    1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3 ****** b. - Square root 256 ,

  3. Math

    1. Which of the following numbers is a rational? A. 4/5 B. square root of 27 C. 4.02002000200002... **** D. Square root of 31 2. Which type of number is shown below? 0.313311333111... A. repeating decimal B. rational C. irrational **** D. terminating

  4. Calculus

    Find the antiderivative of f(x)= the 5th root of x^2. A. the 5th root of (x^3)/3 + C B. (2x^1/5)/ 5 + C C. (5x^7/5)/ 7 + C

  5. math

    I need someone to check a few answers for me, please! 1. Which expression has an approximate value between 6 and 7? Select two answers. A. √36*** B. √38 C. √42*** D. √50 2. How many decimal places does an irrational number have? A. zero B. one C.

  6. Algebra PLEASE?

    Using the numbers 5, 8, and 24, create a problem using no more than four operations (addition, subtraction, multiplication, division, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your

  7. Math Proof

    Prove that square root of 12 is irrational. **I don't know if I did this correctly PF: By contrapositive, assume sqrt(12) is rational. Then there exist an a,b as integers such that a/b is written in the lowest terms, and sqrt(12)=a/b. Then by squaring both

  8. discrete math

    use a direct proof to show that the product of two odd numbers is odd. Proofs: (all the nos. i used are odd) 3 x 3 = 9 5 x 9 = 45 7 x 3 = 21 Yes, but you didn't prove the statement for "all" odd integers, only the odd integers you selected. uhm..he didn't

  9. Math:)

    A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12 radians? a.

  10. ALGEBRA

    SIMPLIFY. ROOT OF 500 SIMPLIFY.ASSUME ALL VARIABLES REPRESENT POSITIVE NUMBERS. ROOT OF X^4Y^3 DECIDE WHETHER ROOT OF 49/100 IS RATIONAL OR IRRATIONAL 500= 100*5 sqrt x^a y^b is x^(a/2) y^(b/2) what is the square root of 7, of 100? are they rational?

  11. math

    1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3 ****** b. - Square root 256 ,

  12. Math (Proof)

    Prove that if ab = ac (mod n) and a is relatively prime to n, then b = c (mod n). Proof: a and n are relatively prime and from ab = ac(mod n), we have n|(ab-ac), so n|a(b-c). Since (a,n)=1 (relatively prime), we get n(b-c). hence b=c(mod n). But what if a

  13. algebra

    simplify: square root of 5 + square root of 20 - square root of 27 + square root of 147. simplify: 6/4square root of 2 sqrt 5 + sqrt 20 - sqrt 27 + sqrt 147 = sqrt 5 + sqrt (4*5) - sqrt (3*9) + sqrt (49*3) = 3 sqrt 5 - 3 sqrt 3 + 7 sqrt 3 = 3 sqrt 5 + 4

  14. Math

    1. Which of the following numbers is a rational? A. 4/5 B. square root of 27 C. 4.02002000200002... **** D. Square root of 31 2. Which type of number is shown below? 0.313311333111... A. repeating decimal B. rational C. irrational **** D. terminating

  15. geometry

    1)given-AB=CD,CD=EF prove-AB-EF (in 5 steps that show why it is corect; i.e two-column proof) 2)Given-

  16. Math

    Here is the question: Is the product of two irrational numbers always an irrational number? Justify your answer. My answer is: No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two

  17. Math

    Check my answers please Is each number rational or irrational 1.-0.6 Rational 2.square root of 40 irrational 3.0.606606660... irrational 4.- square root of 144 rational 5.square root of 12 irrational 6. 0.203040506... irrational

  18. math

    1. Which of the following numbers is a rational? A. 4/5 **** B. square root of 27 C. 4.02002000200002... D. Square root of 31 2. Which type of number is shown below? 0.313311333111... A. repeating decimal B. rational C. irrational*** D. terminating decimal

  19. Math

    Are there more rational or irrational numbers? I am thinking irrational, because the product of a rational and irrational number is irrational. Is this enough of a reason to prove it?

  20. math

    Prove that if x and y are nonnegative real numbers, then (x+y)/2 ≥ sqrt(xy). Use the technique of working backward from the desired conclusion. Where in the proof do we use the fact that x and y are nonnegative?

  21. Math Help please!!

    Could someone show me how to solve these problems step by step.... I am confused on how to fully break this down to simpliest terms sqrt 3 * sqrt 15= sqrt 6 * sqrt 8 = sqrt 20 * sqrt 5 = since both terms are sqrt , you can combine them. sqrt 3* sqrt 15=

  22. Math

    Name ALL sets of numbers to which each number belongs Real Rational Irrational Integer Whole Natural 0 Whole Integer Square root of 5 Irrational -80 Integer 12/3 Rational square root of 100 Irrational square root of 4 Irrational 3pi Irrational

  23. Math

    How can I prove that sqrt(x) > ln x when x > 0? I can quickly see this graphically and intuitively, but how do I do a proof?

  24. math

    im having trouble with radicals, we learned them today but our teacher dint go over what to do with fractions, could u tell me what to do in the square root of 5/36? thx again sqrt (5/36) = (sqrt 5)/sqrt36 = 1/6 * sqrt5 The square root radical applies to

  25. math

    which number has the greatest value? a 3.5 b square root of 15** c square root of 1/16 d 26/100 which number is an irrational number? a 3.5 b square root of 36 c square root of 48 d 37/100*** If a is a rational number and b is an irrational number, then

  26. Calculus

    A) How do you prove that if 0(

  27. Math ~CHECK MY ANSWERS~

    1) Which of these is a rational number? a. Pi b. square root 3 ****** c. square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? A. square root 120, n, square root 3 ****** b. - square root 256,

  28. math

    This is a discussion on Connections Academy Algebra Readiness; Lesson 10 Unit 3. Student A believes the square root of 2 over 8 is a rational number because it can be written as a fraction. Student B believes that the square root of 2 over 8 is an

  29. math

    Factor: x^3 - 3/4x - 1/4 The answer is: (x - 1)(x + 1/2)^2 How do I learn to do that? I'd like to reread an appropriate chapter from an appropriate textbook and do practice problems. It takes experience and practiced eye. Algebra books have chapters on

  30. math

    the two-digit number whose cube root is the square root of the sum of its digits THe cube root of 27 is 3. Only two possible answers; 27 or 64 Looks fairly obvious. 2+7 = 9. Sqrt 9 = 3 and (27)^1/3 = 3. check. 6+ 4 = 10. sqrt 10 = 3+ and (64)^1/3 = 4

  31. math

    solve 2x^2+3x+8=0 and express the solutions in a+bi form. Let's use the quadratic formula to solve for x and express those solutions in a+bi form. x = [-b + or - sqrt(b^2 - 4ac)]/2a Note: sqrt = square root. a = 2, b = 3, and c = 8 from your problem.

  32. discrete math

    If p is prime prove that p^1/2 (root p) is irrational. Generalize the proof that sqrt 2 is irrational. You can find several proofs here: http://www.cut-the-knot.org/proofs/sq_root.shtml You should be able to apply the proof to all square roots of prime

  33. Algebra: Rational Or Irrational

    Hello! My question is 'Is the Square Root of two over 8 a rational or irrational number? At first I thought it was rational because it was written as a fraction, which I thought meant it was rational, but then I realized the square root of two is

  34. Algebra

    SIMPLIFY: ROOT 0F 7 * ROOT OF 14 SIMPLIFY: ROOT OF 1/5 EVALUATE, IF POSSIBLE: ROOT OF 9/16 (I GOT 3/4 BUT I WAS NOT SURE IF THAT WAS CORRECT OR NOT) SIMPLIFY. ASSUME X REPRESENTS A POSITIVE NUMBER: ROOT OF 45X^4 ROOT 0F 7 * ROOT OF 14 = sqrt 7 * sqrt 7 *

  35. math

    determine the area of triangle abc when side ab= square root of x, side bc= square root of x, and side ca= the square root of the square root of x. So how do I solve it. How do I add the square root of x + the square root of x + the square root of the

  36. prime numbers

    Which of these is a prime number? 407, 409, 411, or 413 409 how did you get that? Suppose you are given some number N. If x

  37. algebra

    Solve the question for both the exact irrational root and its rational approximation to the nearest tenth 3h + sqrt 2 = sqrt 5

  38. algebra

    Solve the question for both the exact irrational root and its rational approximation to the nearest tenth. sqrt 2 over 3 s + 1 = sqrt 23 q=

  39. math calculus please help!

    l = lim as x approaches 0 of x/(the square root of (1+x) - the square root of (1-x) decide whether: l=-1 or l=0 or l=1 Let me make sure I understand the question. Do we have lim x->0 x/[sqrt(1+x) - sqrt(1-x)] ? If so then multiply the expression by

  40. algebra 2

    Not sure if either one of these answer are correct to simplify the sqrt for 24 1) 24 = 6 x 4 square root of 24 = square root of 6 x 4 2 root 6 2) sq root 24 = sq root (4x6)= sqrt 4 x sqrt 6= 2sq root 6=4.89898 3) Square root of 24 =sqrt (24) =sqrt(4*6)

  41. Complex numbers

    Prove algebraically that |w+z| is less than or equal to |w|+|z| for any complex numbers w and z, where || is the magnitude. After letting w = a+bi and z = c + di and doing some plugging in etc. I got that ac-bd

  42. Math

    1a) Prove that there exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 1b) use similar idea to prove that there exists a rational number a and an irrational number b so that a^b is irrational 1c)

  43. ALGEBRA

    SIMPLIFY: 5 ROOT OF 6X +4 ROOT OF 6X IS THE ROOT OF 77 IRRATIONAL OR RATIONAL? SIMPLIFY: 8 + ROOT OF 24 DIVIDED BY 2 IS THE ROOT OF 49/100 RATIONAL OR IRRATIONAL AND IS THE ROOT OF 121 RATIONAL OR IRRATONAL? SIMPLIFY: ROOT OF 3X/2 THANKS IN ADVANCE!!!I AM

  44. Algebra

    In this unit, you learned about rational and irrational numbers. The following is a number and two students’ explanations on whether the number is rational or irrational. Square root of 2 over 8 Student A: Square root of 2 over 8 is a rational number

  45. MATH

    For each set of numbers, draw your own number line on a piece of paper, taking care to plot each pair of irrational numbers. Then write a statement comparing the position of the two given numbers on a number line. Also write an inequality comparing the two

  46. Algebra

    Solve for s: h=(square root of 3)times s/2 and solve for h V= (pi)r squared h / 3 Solve for s: h=(square root of 3)times s/2 Multiply both sides by 2. 2h = (sqrt 3)*s*2/2 which cancels the 2 on the right. 2h = (sqrt 3)*s Now divide the right side by

  47. Math(Roots)

    sqrt(24) *I don't really get this stuff.Can somebody please help me? The square root of 24 is 4.898979485566356 I know that..lol,but it says not to use decimals.Here is an example they gave me. Ex.sqrt(18)=sqrt(2*3*3)=3sqrt(2) sqrt[24] = sqrt[4*2*3] =

  48. maths, please help!

    I need help solving this: 6x^2-x-12=0 I usually could do this yet i have completely forgotten what i need to do seeing as there is a number infront of the x^2 This equation is of the general form a x^2 + bx + c = 0 The solution is always x = [-b +/- sqrt

  49. math Please help!!

    1. Which of the following numbers is a rational? A. 4/5 *** B. square root of 27 C. 4.02002000200002... D. Square root of 31 2. Which type of number is shown below? 0.313311333111... A. repeating decimal B. rational *** C. irrational D. terminating decimal

  50. Math

    Can someone help me reword these two things? I don't like how I did them but I can't think of anything else. Thanks!! 1. PROMPT: What do you do to check whether a number is rational or irrational? In your explanation, use an example of an irrational and a

  51. Math of class -10

    Prove that 2/ square root 12is irrational

  52. maths

    prove that the following numbers are irrational:- (i)4 + root 5 ii)4/root3

  53. math

    There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so that a^b is irrational b) prove that if

  54. THE HOMEWORK IS DUE TODAY- HELP! HELP! PLEASE

    There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so that a^b is irrational b) prove that if

  55. please help with math

    There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so that a^b is irrational b) prove that if

  56. ALGEBRA

    CAN YOU PLEASE HELP, I AM STUCK..THANKS FIND THE DISTANCE BETWEEN (-3,2) AND (1,4) DETERMINE WHETHER THE ROOT OF 77 AND THE ROOT OF 121 IS RATIONAL OR IRRATIONAL. THANKS IN ADVANCE, I APPRECIATE ALL OF THE HELP.... The distance between a,b and c,d is

  57. Applied MATH

    As we know the equation 𝑎x≡1 (𝑚od 𝑛) can be solve if and only if (𝑎,𝑛) =1, so 𝑎 and 𝑛 are relatively prime. So, knowing the elements relatively prime to another is somewhat important. Let us call 𝜙(𝑛) the number of positive

  58. radical equation

    2^x+20=15+3^x A)1 B)16 C)-5 D)25 I chose c but i got it wrong i am having a problem understanding it. Let me rewrite the question in a more standard format. 2* sqrt(x)+20=15 + 3*sqrt(x) where * means multiply, and sqrt means the square root. Your use of ^

  59. Math

    How do you find a square root of a number that's not a perfect square? I'm very confused. The book doesn't explain it too well. You can approximate it or simplify it in terms of (products of) square roots of smaller numbers. E.g. consider sqrt[117] The

  60. Algebra-Please help-I'm desperate to understand

    Posted by Megan on Tuesday, October 12, 2010 at 3:44pm. I have a question if someone could help, please explain it. Given b = -1 and h = -1, what is the equation of the graph if the parent function of the radical is y = square root (x) The x should be

  61. math problem

    I'm trying to get a handle on what square roots are (I think that's what they are called). Here is an example. 4(almost like a division sign but it is more like a check mark)3. I don't understand what it is, its a square root? and How do I deal with these

  62. A number thoery question

    Please help me! Thank you very much. Prove Fermat's Last theorem for n=3 : X^3 + Y^3 = Z^3 where X, Y, Z are rational integers, then X, Y, or Z is 0. Hint: * Show that if X^3 + Y^3 = Epsilon* Z^3, where X, Y, Z are quadratic integers in Q[sqrt(-3)], and

  63. IB HL Math

    I need to that if there is better way to prove the following: I am trying to prove that x r = k and k is a multiple of x only when x is prime. I said that if x is non-prime, then: Let a = 6 Let r = 4 6! (6 – 4)! 4! = 3(2) x 5 x 4! (2!) 4! = 15 It is not

  64. Cody

    Write the following with rational, positive exponents. a. sqrt of 8 = 8^1/2 b. seventh root of 5^2 = 5^2/7 c. sqrt sqrt 6 = ??? d. fourth root of sqrt of 5^3 = ??? Can someone please check my work and help with "c and d"? Thanks.

  65. calculus

    A) How do you prove that if 0(

  66. Calculus 3

    I need help writing the series 4 + 1/5 + .3 + 1/(3 + sqrt 2) + 1/(9+ sqrt 3) + 1/(27 + sqrt 4) + 1/(81 + sqrt 5 .... I have played with using irrational numbers, natural log and a vast variety of exponential arrangements. Any help to get me going in the

  67. math

    thanks for the help but i was wondering (16 square root of x-3) times(square root of x-1) is equal to 16x-19 square root of x then plus 3 No, it is not. 16 (sqrt (x-3) ) (sqrt (x-1)) if that is your problem. It is hard to determine from your text. Use

  68. algebra

    a+ sqrt 2 = 7 Solve the question for both the exact irrational root and its rational approximation to the nearest tenth. THANK YOU FOR YOUR TIME AND HELP

  69. algebra

    I'm sorry I don't know how to put in the square root sign...I hope you can understand what I'm getting at : ) multiply and simplify radical expression. square root 7(2square root3 + 3square root7)= ? sqrt 7*(2 sqrt 3 + 3 sqrt 7 = 2 sqrt 21 + 21

  70. Math

    1. Is square root of negative 10 irrational or rational? 2. Is 2.79797979... irrational or rational? I'm not very good at identifying irrational and rational numbers at least I tried too. 1. irrational 2. rational

  71. pre-algebra

    1.Which of the following numbers is an example of an integer? A. -15 B. three-fifths C. start root 7 end root D. 0.252525 . . . 2.Which statement is false? A. Every integer is a real number. B. The number zero is a rational number. C. Every irrational

  72. calculus

    prove that d/dx 4x .√(x + √x) = 6x+5 (x)1/2/√(x + √x) solution is d/dx 4x.[x+(x)1/2]1/2 = d/dx 4x.[x+(x)^1/2]^1/2 d/dx 4x.[x+(x)^1/2]^1/2 Product Rule = 4x[1/2(x+(x)^1/2)^-1/2 * (1+1/2x^-1/2) +[x+(x)^1/2]^1/2*4 d/dx(4 x sqrt(x+sqrt(x))) = (2 (1/(2

  73. Physics

    Hello everyone, I have made measurements of the periods of a pendulum attached to a stationary point at a certain height h. When plotting the periods as a function of the square root of the length minus the height it gives us a straight line. I now need to

  74. Modern algebra

    Prove that a cyclic group with prime order p has two subgroups. Firstly, I know that the two groups are the trivial group and itself. I don't know how to start the proof.

  75. math

    1. Rosa, Roberto, Andrea, and Inno find an estimate for the square root of 10. Who has proposed the best solution? a. Rosa: "Use the sqaure root of 9 and the square root of 25 to estimate." b. Roberto: "I will use the square root of 4 and the sqaure root

  76. MATH

    1/(X^-2Y)-1(XY^-2)=____ XY (square root of 84 - square root of 5.25) I don't understand the first equation. sqrt(84)=sqrt(4*21)=sqrt(16*5.25)=4sqrt(5.25) so sqrt(84)-sqrt(5.25)= 4sqrt(5.25)-sqrt(5.25)=3sqrt(5.25)

  77. DISCRETE MATHS

    Prove that for every set S, Ø \subseteq( S. i need to Use vacuous proof. i know that vacuous proof is when the hypothesis is always False. but for this i find it very difficult please can you help me prove this? thanks.

  78. College Algebra--Still Confused

    I have a few problems I need help with and also do have multiple choice. If I can have an explanation of how to get the answer that would be great. 1. Use the discriminant to determine whether the given equation has two irrational roots, two rational

  79. College Algebra

    I have a few problems I need help with and also do have multiple choice. If I can have an explanation of how to get the answer that would be great. 1. Use the discriminant to determine whether the given equation has two irrational roots, two rational

  80. calculus

    A) How do you prove that if 0(

  81. calculus

    A) How do you prove that if 0(

  82. imp4

    Pow 3 "a sticky gum" revisited Gumballs are 1 penny each. The kids each want a different color. what is the maximum spent with each generalization. create formulas for the following. Generalize the number of children. Generalize the number of gum ball each

  83. Calculus

    After an hour of googling this as you suggested, I still can't find the discussions or proof you were referring to. Can you please either send the link you found or help me with this? I don't know how to even start it. Prove that the function defined by:

  84. Algebra

    For what value(s) of b will x^2 + bx + 3 have exactly one root? I'm rather new at this but wouldn't b=2*sqrt(3) give (x+sqrt3)2 as factors and that would give one root? Check my thinking. for a quadratic equation to have exactly one root, the discriminat

  85. Elementary Euclidean Geometry(Math)

    Little Joseph once said: I was once asked to prove that (PROOF ONE) in a right triangle, the sum of the squares of two sides equals the square of the third. Smart little rascal that I am, I proved it with ease. I was then asked to prove that (PROOF 2) if

  86. Real Analysis (Math)

    Prove: [1/sqrt(2)] [sqrt(a) + sqrt(b)]

  87. MATH (SURDS)

    we have been asked to prove that it is possible to determine the value of a surd using either similar figures or Pythagoreans theorem. we have been shown how to construct the surd using a compass and ruler. but we now have to prove that our method is

  88. Algebra

    which of these numbers can be classified as both real and irrational? 1. 5.858585858 2. 63.4 3. root 21 4. root 36 which is both a real number and an integer? 1. 23 2. 1/4 3. root 27 4. 3.402538 which of these number is classified as both real and

  89. nonlinear algebra

    Use prime factorization to simplify the following square root leave as exact answer. How do you find the prime factors of this problem? 112 square root

  90. Algebra

    Is there any prime number whose root is an integer? I meant to say Square Root Nevermind I figured it out. Good work. If a prime number by definition has no factors, ...

  91. math,correction

    the problem reads: evaluate sqrt (-4) if possible. my answer: sqrt (-4)

  92. Math help plz ASAP.

    Rationalize each denominator. 6 + square root of 2 ____________________________ square root of 3 PLZ HELP..dont kno how to do this question.plz explain..thanks You have (6 + sqrt(2))/sqrt(3) multiply that by sqrt(3)/sqrt(3) to get [(6 + sqrt(2))*sqrt(3)]/3

  93. math,algebra,help

    Directions are simplify by combining like terms. x radiacal 18 -3 radical 8x^2 can someone show me how to do these types of problems. thanks I cant determine the second term. For the first, I think you meant x sqrt(18) which reduces to x sqrt (9*3) or 3x

  94. pre-algebra

    Using the numbers 5, 8, and 24, create a problem using no more than four operations (addition, subtraction, multiplication, division, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your

  95. Math, algebra!! Please help!!!!!!

    Using the numbers 5, 8, and 24, create a problem using no more than four operations (addition, subtraction, multiplication, division, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your

  96. Algebra 8th grade please help!!!!!!

    Using the numbers 5, 8, and 24, create a problem using no more than four operations (addition, subtraction, multiplication, division, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your

  97. math

    Using the numbers 5, 8, and 24, create a problem using no more than four operations (addition, subtraction, multiplication, division, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your

  98. Math

    Using the numbers 5, 8, and 24 create a problem using no more than four operations (addition, subtraction, multiplication, division, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your

  99. Math

    Using numbers 5,8 and 24 create a problem using no more than four operations(additions, multiplication, division, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your operations is an

  100. Algebra

    1 last square root : Rationalize the denominator 5/sqrt[3]+sqrt[5]= 5*sqrt[3]-sqrt[5]/ sqrt[3]sqrt5[5]*sqrt[3]-sqrt[5]= 5sqrt[3]-5sqrt[5]/sqrt[9]-sqrt[15]+sqrt[15]- sqrt[25]= 5sqrt[3]-5sqrt[5]/-16 = 5sqrt[3]-5sqrt[5]/ -2

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