# PSAT Math : Basic Squaring / Square Roots

## Example Questions

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

Simplify the expression:

The expression cannot be siimplified further.

Explanation:

For each of the expressions, factor out a perfect square:

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

Simplify:

The expression cannot be simplified further.

Explanation:

Simplify each of the radicals by factoring out a perfect square:

### Example Question #3 : How To Add Square Roots

Add the square roots into one term:

Explanation:

In order to solve this problem we need to simplfy each of the radicals. By doing this we will get two terms that have the same number under the radical which will allow us to combine the terms.

### Example Question #4 : How To Add Square Roots

Simplify:

Explanation:

Remember that you treat square roots like you do variables in the sense that you just add the like factors. In this problem, the only set of like factors is the pair of  values.  Hence:

Do not try to simplify any further!

### Example Question #5 : How To Add Square Roots

Simplify:

Explanation:

Begin by simplifying your more complex roots:

This lets us rewrite our expression:

Do the basic multiplications of coefficients:

Reorder the terms:

Finally, combine like terms:

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

Multiply and simplify. Assuming all integers are positive real numbers.

Explanation:

Multiply the coefficents outside of the radicals.

Then multiply the radicans. Simplify by checking for a perfect square.

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

Mulitply and simplify. Assume all integers are positive real numbers.

Explanation:

Order of operations, first distributing the  to all terms inside the parentheses.

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

The square root(s) of 36 is/are ________.

-6

6 and -6

6, -6, and 0

None of these answers are correct.

6

6 and -6

Explanation:

To square a number is to multiply that number by itself. Because 6 x 6 = 36 AND -6 x -6 = 36, both 6 and -6 are square roots of 36.

### Example Question #4 : How To Multiply Square Roots

Simplify:

Explanation:

Multiplication of square roots is easy! You just have to multiply their contents by each other. Just don't forget to put the result "under" a square root! Therefore:

becomes

Now, you need to simplify this:

You can "pull out" two s.  (Note, that it would be even easier to do this problem if you factor immediately instead of finding out that .)

After pulling out the s, you get:

Solve for :