What's the Square Root of 75?

Date: 08/18/2002 at 00:03:18
From: Priss Edwards
Subject: Sqrt 75

It's been years since I've been in college and my daughter needs 
help. Is the sqrt 75  

   15* sqrt 5 
or 
    5* sqrt 15, 

or what? And why?

Thanks for your help.

Priss

P.S. I've bookmarked this site for my daughter.

Date: 08/18/2002 at 01:14:48
From: Doctor Paul
Subject: Re: Sqrt 75

Write 75 as a product of primes:

   75 = 3*5*5

So sqrt(75) = sqrt(3*5*5)

Whenever you have two of the same number inside the square root, you 
can bring one of them outside and remove the other. Thus
sqrt(75) = 5*sqrt(3).

Another example:

   sqrt(6048) = sqrt(2*2*2*2*2*3*3*3*7) = 2*2*3*sqrt(2*3*7) = 

   12*sqrt(42)

I hope this helps.  Please write back if you'd like to talk about 
this some more.

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