# PSAT Math : How to simplify square roots

## Example Questions

### Example Question #2 : Factoring And Simplifying Square Roots

Simplify. Assume all variables are positive real numbers.

Explanation:

The index coefficent in is represented by . When no index is present, assume it is equal to 2.  under the radical is known as the radican, the number you are taking a root of.

First look for a perfect square,

Take your exponents on both variables and determine the number of times our index will evenly go into both.

So you would take out a  and would be left with a

*Dividing the radican exponent by the index - gives you the number of variables that should be pulled out.

The final answer would be .

### Example Question #3 : Factoring And Simplifying Square Roots

Simplify. Assume all integers are positive real numbers.

Explanation:

Index of means the cube root of Radican

Find a perfect cube in

Simplify the perfect cube, giving you .

Take your exponents on both variables and determine the number of times our index will evenly go into both.

### Example Question #4 : Factoring And Simplifying Square Roots

Simplify square roots. Assume all integers are positive real numbers.

Simplify as much as possible. List all possible answers.

1a.

1b.

1c.

and

and  and

and  and

and  and

and  and

Explanation:

When simplifying radicans (integers under the radical symbol), we first want to look for a perfect square. For example, is not a perfect square. You look to find factors of  to see if there is a perfect square factor in , which there is.

1a.

Do the same thing for .

1b.

1c.Follow the same procedure except now you are looking for perfect cubes.

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

Simplify

÷ √3

2

3√3

none of these

3

not possible

3√3

Explanation:

in order to simplify a square root on the bottom, multiply top and bottom by the root

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

Simplify:

√112

20

4√10

10√12

4√7

12

4√7

Explanation:

√112 = {√2 * √56} = {√2 * √2 * √28} = {2√28} = {2√4 * √7} = 4√7

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

Simplify:

√192

4√3
4√2
8√2
8√3
None of these
Explanation:

√192 = √2 X √96

√96 = √2 X √48

√48 = √4 X√12

√12 = √4 X √3

√192 = √(2X2X4X4) X √3

= √4X√4X√4  X √3

= 8√3

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

What is the simplest way to express ?

Explanation:

First we will list the factors of 3888:

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

Simplify:

Explanation:

4√27 + 16√75 +3√12 =

4*(√3)*(√9)  + 16*(√3)*(√25)  +3*(√3)*(√4) =

4*(√3)*(3) + 16*(√3)*(5) + 3*(√3)*(2) =

12√3  + 80√3 +6√3= 98√3

Simplify: