Adding Radicals

Date: 9/11/96 at 22:33:11
From: Anonymous
Subject: Adding Radicals

I have absolutely no idea how to add radicals.  I can multiply 
and divide fine, but I can't add.  Problems witn obvious answers 
(root 81 + root 25) I can do, but problems not involving perfect 
squares I can't do.

Date: 9/12/96 at 11:37:2
From: Doctor Beth
Subject: Re: Adding Radicals

One thing to remember when adding radicals is that only the ones that 
are alike can be added together.  So for example, you can't do 
anything to simplify root(3) + root(5) because 3 and 5 are different 
numbers.  The only time that you can add radicals together is if they 
have the same number under them:  like 
2*root(2) + 3*root(2) = 5*root(2).  

This works just the same way that you can add 2x +3x = 5x.  Taking 
that a little further, if the radicals can be simplified in a way to 
make them have the same number inside them, then you can also add 
them. For example, if I wanted to simplify root(8) + root(32), I 
would first simplify root(8) as root(2*2*2) which equals 2*root(2).  
Then I'd also recognize that root(32)=root(4*4*2)=4*root(2).  
(Basically, when I try to simplify square roots, I look for perfect 
squares that are inside them.)  Now I have
root(8)+root(32) = 2*root(2)+4*root(2) = 6*root(2).

I hope this helps!

-Doctor Beth,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/