SOLUTION: Hello! I have these few problems and just want to make sure I have them correct. 1. Find the root if it is a real number: Square Root -561 Is this defined as NOT A REAL NUM

Algebra ->  Radicals -> SOLUTION: Hello! I have these few problems and just want to make sure I have them correct. 1. Find the root if it is a real number: Square Root -561 Is this defined as NOT A REAL NUM      Log On


   



Question 338554: Hello!
I have these few problems and just want to make sure I have them correct.
1. Find the root if it is a real number:
Square Root -561
Is this defined as NOT A REAL NUMBER?
2. Find the root if it is a real number:
Index is 4 and negative sign is outside the root
With 81 as the square root inside
Is this defined as -3?
3. Simplify the root.
Negative on the outside, square root x^28
Is this defined as -x^14?
or is it defined as |-x^14|?
4. Simplify the first converting to rational exponents. Assume that all variables represent positive real numbers.
Square Root z^28
Is this defined as z^14?
I'm confuse on whether it will be an absolute value with | | or divide them by 2?
Thank you!


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. Find the root if it is a real number:
Square Root -561
Is this defined as NOT A REAL NUMBER?
-561 is a real number
sqrt%28-561%29+=+sqrt%28-1%29%2Asqrt%28561%29
= isqrt%28561%29 All you can do.
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2. Find the root if it is a real number:
Index is 4 and negative sign is outside the root
With 81 as the square root inside
Is this defined as -3?
81 is a real number, and it have 4 4th roots.
sqrt%28sqrt%2881%29%29 = ± sqrt%289%29 and ± sqrt%28-9%29
= ± 3 and ± 3i
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3. Simplify the root.
Negative on the outside, square root x^28
Is this defined as -x^14?
or is it defined as |-x^14|?
Just -x^14
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4. Simplify the first converting to rational exponents. Assume that all variables represent positive real numbers.
Square Root z^28
Is this defined as z^14?
It is.
----------
I'm confuse on whether it will be an absolute value with | | or divide them by 2? No absolute values involved.