PSAT Math : Factoring and Simplifying Square Roots

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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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 #11 : Factoring And Simplifying 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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