Associated Topics || Dr. Math Home || Search Dr. Math

```
Date: 9/11/96 at 22:33:11
From: Anonymous

I have absolutely no idea how to add radicals.  I can multiply
(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

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/
```
Associated Topics:
Middle School Square Roots

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search