PSAT Math : How to simplify square roots

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Simplify Square Roots

Simplify. Assume all variables are positive real numbers. 

Possible Answers:

Correct answer:

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, 

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 : How To Simplify Square Roots

Simplify. Assume all integers are positive real numbers. 

Possible Answers:

Correct answer:

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.

 


The final answer would be

Example Question #3 : How To Simplify 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 

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 : Simplifying Square Roots

Simplify

÷ √3

Possible Answers:

not possible

3√3

none of these

2

3

Correct answer:

3√3

Explanation:

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

Asatsimplifysquare_root

Example Question #5 : How To Simplify Square Roots

Simplify:

√112

Possible Answers:

12

4√7

10√12

20

4√10

Correct answer:

4√7

Explanation:

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

Example Question #3 : Factoring And Simplifying Square Roots

Simplify:

 

√192

Possible Answers:
8√3
4√2
4√3
8√2
None of these
Correct answer: 8√3
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 #3 : Simplifying Square Roots

What is the simplest way to express \sqrt{3888}?

Possible Answers:

12\sqrt{27}

144\sqrt{27}

2\sqrt{972}

2304\sqrt{2}

Correct answer:

Explanation:

First we will list the factors of 3888:

3888=3\times1296=3\times\3\times432=3^2\times12\times36=3^2\times12\times12\times3=3^2\times12^2\times3

Example Question #1 : How To Simplify Square Roots

Simplify:

 

Possible Answers:

Correct answer:

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

Example Question #4 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

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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