# SAT Math : How to add square roots

## Example Questions

### Example Question #1 : How To Add Square Roots

If  what is ?

Explanation:

Square both sides:

x = (32)2 = 92 = 81

### Example Question #2 : How To Add Square Roots

Explanation:

To simplify, break down each square root into its component factors:

You can remove pairs of factors and bring them outside the square root sign. At this point, since each term shares , you can add them together to yield the final answer:

### Example Question #21 : Basic Squaring / Square Roots

Simplify:

Explanation:

Take each fraction separately first:

(2√3)/(√2) = [(2√3)/(√2)] * [(√2)/(√2)] = (2 * √3 * √2)/(√2 * √2) = (2 * √6)/2 = √6

Similarly:

(4√2)/(√3) = [(4√2)/(√3)] * [(√3)/(√3)] = (4√6)/3 = (4/3)√6

√6 + (4/3)√6 = (3/3)√6 + (4/3)√6 = (7/3)√6

### Example Question #21 : Basic Squaring / Square Roots

Simplify the following expression:

Explanation:

Begin by factoring out each of the radicals:

For the first two radicals, you can factor out a  or :

The other root values cannot be simply broken down. Now, combine the factors with :

Solve for .

Note, :