### All PSAT Math Resources

## Example Questions

### Example Question #1 : Factoring And Simplifying Square Roots

Simplify. Assume all variables are positive real numbers.

**Possible Answers:**

**Correct answer:**

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,

Then to your Variables

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 #2 : Factoring And Simplifying Square Roots

Simplify. Assume all integers are positive real numbers.

**Possible Answers:**

**Correct answer:**

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.

The final answer would be

### 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.

**Possible Answers:**

and and

and and

and

and and

**Correct answer:**

and and

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 : Factoring And Simplifying Square Roots

Simplify

9 ÷ √3

**Possible Answers:**

2

3

not possible

none of these

3√3

**Correct answer:**

3√3

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

### Example Question #1 : Factoring And Simplifying Square Roots

Simplify:

√112

**Possible Answers:**

20

4√10

12

4√7

10√12

**Correct answer:**

4√7

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

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

Simplify:

√192

**Possible Answers:**

**Correct answer:**8√3

√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 #2 : How To Simplify Square Roots

What is the simplest way to express ?

**Possible Answers:**

**Correct answer:**

First we will list the factors of 3888:

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

Simplify:

**Possible Answers:**

**Correct answer:**

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

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

Simplify:

**Possible Answers:**

**Correct answer:**

To simplify a square root, you can break the number down into its prime factors using a factor tree. The prime factors of 72 are . Let's take each piece separately.

The square root of can be simplified to be which is the same as .

The square root of is .

When you multiply together your answers,

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