PSAT Math : How to find the common factors of squares

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Find The Common Factors Of Squares

Solve for \dpi{100} x:

x\sqrt{45}+x\sqrt{72}=\sqrt{18}

Possible Answers:

x=\frac{\sqrt{2}}{\sqrt{5}+2\sqrt{2}}

x=\frac{\sqrt{2}}{\sqrt{5}}+\frac{1}{2}

x=\sqrt{9}

x=\frac{\sqrt{5}}{\sqrt{2}}+2

x=3

Correct answer:

x=\frac{\sqrt{2}}{\sqrt{5}+2\sqrt{2}}

Explanation:

x\sqrt{45}+x\sqrt{72}=\sqrt{18}

Notice how all of the quantities in square roots are divisible by 9

x\sqrt{9\times 5}+x\sqrt{9\times 8}=\sqrt{9\times 2}

x\sqrt{9}\sqrt{5}+x\sqrt{9}\sqrt{4\times 2}=\sqrt{9}\sqrt{2}

3x\sqrt{5}+3x\sqrt{4}\sqrt{2}=3\sqrt{2}

3x\sqrt{5}+6x\sqrt{2}=3\sqrt{2}

x(3\sqrt{5}+6\sqrt{2})=3\sqrt{2}

x=\frac{3\sqrt{2}}{3\sqrt{5}+6\sqrt{2}}

Simplifying, this becomes

x=\frac{\sqrt{2}}{\sqrt{5}+2\sqrt{2}}

Example Question #2 : Factoring And Simplifying Square Roots

If m and n are postive integers and 4m = 2n, what is the value of m/n?

Possible Answers:

2

1/2

4

8

16

Correct answer:

1/2

Explanation:
  1. 2= 4. Also, following the rules of exponents, 4= 1. 
  2. One can therefore say that m = 1 and n = 2.
  3. The question asks to solve for m/n. Since m = 1 and n = 2, m/n = 1/2.

Example Question #2 : How To Find The Common Factors Of Squares

Simplify the radical:

Possible Answers:

Correct answer:

Explanation:

 

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