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/