State if each number is Rational,Irrational,or not a real number?
1.)square root of 9/16
2.) square root of -9
3.)square root of -16 divided by -4
4.)square root of -8(-2)
5.)square root of 25 divided by 8
6.)square root of -1/4
Please Help! I have been sick for 4 weeks and I still don't get this assignment.
the smallest set is the natural numbers: 1,2,3,...
Next is whole numbers: 0,1,2,3,4...
Next is integers: ...-2,-1,0,1,2,...
Next is rational: these are all the fractions 1/2, 3/7, and so on
Next is irrational: everything else
Real numbers include all of the above
Finally there are the complex numbers which include all the real numbers, as well as imaginary ones
√(9/16) = √9/√16 = 3/4: rational
√-9 = √9√-1 = 3i: not real (complex)
√(-16/-4) = √4 = 2: rational
√-16/-4 = 4i/4 = i: not real
√((-8)(-2)) = √16 = 4: rational
(√-8)(-2) = 2√2 i (-2) = -4√2i: not real
√25/8 = 5/8: rational
√(-1/4) = (√-1)/2 = -1/2 i: not real
As you can see above, it is necessary to use parentheses sometimes, to make it clear just what you mean.
1.) Rational - The square root of 9/16 is 3/4, which is a rational number since it can be expressed as a ratio of two integers.
2.) Not a real number - The square root of -9 is an imaginary number since it involves the square root of a negative number.
3.) Rational - The square root of -16 divided by -4 is 2, which is a rational number.
4.) Not a real number - Since -8(-2) is a negative number multiplied by a negative number, the square root of it results in an imaginary number.
5.) Rational - The square root of 25/8 simplifies to 5/√8. While √8 is irrational, 5/√8 is still a rational number as it can be expressed as a ratio of two integers.
6.) Not a real number - The square root of -1/4 is an imaginary number since it involves the square root of a negative number. But hey, at least it's imaginary and not real, so nothing to worry about!
Sure! I'll help you with each number step by step:
1.) The square root of 9/16 is a rational number because both the numerator (9) and the denominator (16) are perfect squares.
2.) The square root of -9 is not a real number because square roots of negative numbers are not defined within the real number system. However, it can be expressed as an imaginary number, which is written as √(-9) = 3i.
3.) The square root of -16 divided by -4 can be simplified step-by-step:
- √(-16) = √(16) * √(-1) = 4i, where i is the imaginary unit
- Dividing 4i by -4, we get -4i, which is also an imaginary number.
4.) The expression square root of -8(-2) can be simplified step-by-step:
- √(-8) = √(8) * √(-1) = 2√2i
- Multiplying 2√2i by -2, we get -4√2i.
5.) The square root of 25 divided by 8 is a rational number. √25 = 5, and dividing 5 by 8 gives us 5/8.
6.) The square root of -1/4 can be simplified step-by-step:
- √(-1/4) = √1 * √(-1) * √(1/4) = i/2, where i is the imaginary unit.
I hope this helps! Let me know if you have any further questions.
I'm sorry to hear that you've been sick. Don't worry, I'm here to help you with your assignment. Let's determine whether each number is rational, irrational, or not a real number.
1.) Square root of 9/16:
To determine if this number is rational, irrational, or not a real number, we first simplify the square root of 9/16:
√(9/16) = √9 / √16 = 3/4
Since 3/4 is a fraction, it is a rational number.
2.) Square root of -9:
To determine if this number is rational, irrational, or not a real number, we should consider that the square root of a negative number is not defined in the set of real numbers. Therefore, the square root of -9 is not a real number.
3.) Square root of -16 divided by -4:
Let's simplify this expression first:
√(-16) / -4 = √(-1 * 4 * 4) / -4 = 2i / -4 = -i/2
Since -i/2 is in the form of a complex number (i is the imaginary unit, where i^2 = -1), it is not a real number.
4.) Square root of -8(-2):
Let's simplify this expression first:
√(-8 * -2) = √(16) = 4
Since 4 is a whole number, it is a rational number.
5.) Square root of 25 divided by 8:
Let's simplify this expression first:
√(25) / 8 = 5/8
Since 5/8 is a fraction, it is a rational number.
6.) Square root of -1/4:
To determine if this number is rational, irrational, or not a real number, we should consider that the square root of a negative number is not defined in the set of real numbers. Therefore, the square root of -1/4 is not a real number.
In summary,
1.) √(9/16) is a rational number.
2.) √(-9) is not a real number.
3.) √(-16) / -4 is not a real number.
4.) √(-8(-2)) is a rational number.
5.) √(25) / 8 is a rational number.
6.) √(-1/4) is not a real number.