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### Powers of Roots

Date: 05/14/2001 at 11:47:31
From: Angel Doll
Subject: Exponents before square roots

What do you do when you have a small number in front of a square root?
For example: 3(except it's a little three)sqrt of -216.

Thank you very much,
Angel

Date: 05/14/2001 at 12:24:39
From: Doctor Douglas
Subject: Re: Exponents before square roots

Hi Angel, and thanks for writing.

The little number tells you the power of the root that is being taken.
If the number is a 3, for example, then we are talking about a cube
root. If the number is a 2, or is missing, then we are talking about a
square root.
____
/
/\  /  64    = 8       the square root of 64 is 8.
\/
____
3 /
/\  / -125   = -5      the cube root of -125 is -5.
\/
____
7 /  7
/\  / 10     = 10      the seventh root of ten million is 10.
\/
_____
2 / 4 2      2
/\  / x y    = x y     the square root of x^4 y^2 is x^2 y.
\/

I hope this helps. Please write back if you have more questions about
this.

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/

Associated Topics:
Middle School Square Roots

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