Add 5sqrt(10) + sqrt(10)
To add 5sqrt(10) and sqrt(10), we combine the terms with the same radical, which in this case is sqrt(10).
5sqrt(10) + sqrt(10) = (5 + 1) sqrt(10) = 6sqrt(10)
11sqrt(19) - 5sqrt(19)
To subtract 5sqrt(19) from 11sqrt(19), we again combine the terms with the same radical, which in this case is sqrt(19).
11sqrt(19) - 5sqrt(19) = (11 - 5) sqrt(19) = 6sqrt(19)
5sqrt(19) * 6sqrt(2)
To multiply 5sqrt(19) by 6sqrt(2), we can simply multiply the coefficients (numbers outside the radical) and the radicals (numbers inside the radical):
5sqrt(19) * 6sqrt(2) = (5 * 6) * sqrt(19 * 2) = 30sqrt(38)
divide sqrt(95) with a denominator of 3sqrt(5)
To divide sqrt(95) by 3sqrt(5), we need to rationalize the denominator, which means eliminating the radical from the denominator.
First, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of 3sqrt(5) is -3sqrt(5).
(sqrt(95) * -3sqrt(5)) / (3sqrt(5) * -3sqrt(5))
This simplifies to:
-3sqrt(475) / -9 * 5
Further simplifying:
sqrt(475) / 15
Finally, sqrt(475) cannot be simplified since there are no perfect square factors. Therefore, the answer is:
sqrt(475) / 15
is that right?
Apologies for the mistake in the previous response. Let's correct it.
To divide sqrt(95) by 3sqrt(5), we can multiply the numerator and denominator by the conjugate of the denominator, which is also 3sqrt(5). This will help eliminate the radical from the denominator.
(sqrt(95) * 3sqrt(5)) / (3sqrt(5) * 3sqrt(5))
Simplifying this expression gives:
3sqrt(475) / 9 * 5
Further simplifying:
sqrt(475) / 45
Therefore, the correct answer is:
sqrt(475) / 45
divide 36sqrt(39) with a denominator of 9sqrt(13)
To divide 36sqrt(39) by 9sqrt(13), we follow the same steps as before to rationalize the denominator.
Multiply both the numerator and denominator by the conjugate of the denominator, which is also 9sqrt(13).
(36sqrt(39) * 9sqrt(13)) / (9sqrt(13) * 9sqrt(13))
Simplifying this expression gives:
324sqrt(507) / 81 * 13
Further simplifying:
4sqrt(507) / 13
Therefore, the division of 36sqrt(39) by 9sqrt(13) is:
4sqrt(507) / 13
Simplify sqrt(48)
Let's simplify sqrt(48).
First, we look for perfect square factors of 48. We find that 16 is a perfect square that divides evenly into 48.
sqrt(48) = sqrt(16 * 3)
Next, we can rewrite the expression using the product rule of square roots:
sqrt(16 * 3) = sqrt(16) * sqrt(3)
Since the square root of 16 is 4:
sqrt(16) * sqrt(3) = 4 * sqrt(3)
Therefore, sqrt(48) simplifies to 4sqrt(3).
simplify third root (54)
To simplify the cube root of 54, we need to find the prime factors of 54 and group them in sets of three.
The prime factorization of 54 is: 2 * 3^3.
Now we can group the factors in sets of three: 2 * (3^3) = 2 * (3 * 3 * 3).
Taking the cube root of each set gives us:
cube root of 2 * cube root of (3 * 3 * 3) = 2 * 3 = 6.
Therefore, the simplified form of the cube root of 54 is 6.
simplify thirdroot(54)
To simplify the cube root of 54, we can find the prime factorization of 54 and then group the factors in sets of three.
The prime factorization of 54 is 2 * 3^3.
Now we can group the factors in sets of three: 2 * (3 * 3 * 3) = 2 * (27).
Taking the cube root of each set gives us:
Cube root of 2 * Cube root of 27 = 2 * 3 = 6.
Therefore, the simplified form of the cube root of 54 is 6.
What is the irrational square root sqrt(63) rewritten as the product of an integer and another irrational square root, in simplest form?
To rewrite the square root of 63 as the product of an integer and another irrational square root, we need to find the largest perfect square that divides evenly into 63. In this case, it is 9.
We can express 63 as 9 * 7:
sqrt(63) = sqrt(9 * 7)
Using the property of square roots, we can separate the perfect square factor:
sqrt(9 * 7) = sqrt(9) * sqrt(7)
The square root of 9 is 3, so we have:
sqrt(9) * sqrt(7) = 3 * sqrt(7)
Hence, sqrt(63) can be rewritten as 3 multiplied by the square root of 7: 3sqrt(7).
What is the irrational cube root thirdroot(81) rewritten as a product of an integer and another irrational cube root?
To rewrite the cube root of 81 as the product of an integer and another irrational cube root, we need to find the largest perfect cube that divides evenly into 81. In this case, it is 27.
We can express 81 as 27 * 3:
thirdroot(81) = thirdroot(27 * 3)
Using the property of cube roots, we can separate the perfect cube factor:
thirdroot(27 * 3) = thirdroot(27) * thirdroot(3)
The cube root of 27 is 3, so we have:
thirdroot(27) * thirdroot(3) = 3 * thirdroot(3)
Therefore, the cube root of 81 can be rewritten as 3 multiplied by the cube root of 3: 3*thirdroot(3).
sqrt(169)
The square root of 169 is 13.
Therefore, sqrt(169) = 13.
find the cube root of -729
The cube root of -729 is -9.
Therefore, the cube root of -729 is -9.
find the cube root of -8
The cube root of -8 is -2.
Therefore, the cube root of -8 is -2.
cubic root of 135
The cube root of 135 is approximately 5.207.
Find the cubic root of 135
A. thirdroot(5)
B. 3sqrt(5)
C. 3thridroot(5)
D. 5thirdroot(27)
To find the cubic root of 135, we can use a calculator or simplify it manually by prime factorization.
The prime factorization of 135 is 3 * 3 * 3 * 5.
To take the cubic root, we need to group the factors in sets of three:
cubic root of (3 * 3 * 3 * 5) = cubic root of (3^3 * 5)
Using the property of the cubic root, we can write:
cubic root of (3^3 * 5) = 3 * cubic root of 5
Hence, the cubic root of 135 is equivalent to option C: 3 * thirdroot(5).
Rewrite the irrational cube root of thirdroot(189) as the product of an integer and another irrational cube root. please show the work
To rewrite the irrational cube root of thirdroot(189) as the product of an integer and another irrational cube root, we need to find the largest perfect cube that divides evenly into 189. In this case, it is 27.
We can express 189 as 27 * 7:
thirdroot(189) = thirdroot(27 * 7)
Using the property of cube roots, we can separate the perfect cube factor:
thirdroot(27 * 7) = thirdroot(27) * thirdroot(7)
The cube root of 27 is 3, so we have:
thirdroot(27) * thirdroot(7) = 3 * thirdroot(7)
Therefore, the cube root of thirdroot(189) can be rewritten as 3 multiplied by the cube root of 7: 3 * thirdroot(7).
Is that correct?
Apologies for the incorrect response. Let's correct it.
To rewrite the cube root of thirdroot(189) as the product of an integer and another irrational cube root, we need to find the largest perfect cube that divides evenly into 189. In this case, it is 27.
We can express 189 as 27 * 7:
thirdroot(189) = thirdroot(27 * 7)
Using the property of cube roots, we can separate the perfect cube factor:
thirdroot(27 * 7) = thirdroot(27) * thirdroot(7)
The cube root of 27 is 3, so we have:
thirdroot(27) * thirdroot(7) = 3 * thirdroot(7)
Hence, the cube root of thirdroot(189) can be rewritten as 3 multiplied by the cube root of 7: 3 * thirdroot(7).
Therefore, the revised answer is correct.
There are 3 wrong answers. I'll list the answers bellow to make it easier.
1) 6sqrt(10)
2) 6sqrt(19)
3) 30sqrt(38)
4) sqrt(19) denominator 3
5) 4sqrt(3)
6) 4sqrt(3)
7) 3thirdroot(2)
8) sqrt(7)
9) 3thirdroot(3)
10) 13
11) -9
12) -2
13) 3thirdroot(5)
the teacher already answered 14 in the intro page but the answer to 14 is 14.13 if you didn't see it, and I cant answer the last one yet and ill forget that I made this by the time it is, so sorry if its wrong!!
-Fruity :3
Apologies for the earlier mistakes. Let's go through each question and provide the correct answer:
1) The square root of 169 is 13.
2) The cube root of 135 is 5thirdroot(3).
3) The cube root of -729 is -9.
4) The cube root of -8 is -2.
5) The cube root of thirdroot(189) is 3thirdroot(7).
6) The square root of 48 is 4sqrt(3).
7) The square root of 95 divided by 3sqrt(5) is sqrt(19) / sqrt(5), which can be further simplified as sqrt(19/5).
8) The square root of 63 is 3sqrt(7).
9) The cube root of thirdroot(54) is 3thirdroot(2).
10) The cube root of 135 is 5thirdroot(3).
11) The cube root of -8 is -2.
12) The cube root of 81 is thirdroot(27) = 3.
13) The cubic root of -729 is -9.
14) The irrational cube root of thirdroot(189) is 3thirdroot(7).
15) The answer is yet to be determined, so we cannot provide an answer for this question.
Please double-check the numbering of the questions to ensure that the correct response is attributed to each one.