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SAT Math : Square Roots and Operations

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #21 : Square Roots And Operations

Evaluate: $\sqrt{108}-\sqrt{81}$

Possible Answers:

$6\sqrt{3}-9$

None of the available answers

$24\sqrt{3}-9$

$4\sqrt{27}-\sqrt{9}$

$24\sqrt{3}-81$

Correct answer:

$6\sqrt{3}-9$

Explanation:

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= 2^2\times 3\times 9= 2^2\times 3^2\times 3$

$81=9\times 9=9^2$

$\sqrt{108}-\sqrt{81}=6\sqrt{3}-9$

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Example Question #1 : How To Divide Square Roots

(√27 + √12) / √3 is equal to

Possible Answers:

(6√3)/√3

5/√3

√3

Correct answer:

Explanation:

√27 is the same as 3√3, while √12 is the same as 2√3.

3√3 + 2√3 = 5√3

(5√3)/(√3) = 5

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Example Question #91 : Arithmetic

Simplify: $\frac{\sqrt{210}}{\sqrt{6}}$

Possible Answers:

$7\sqrt{5}$

$\sqrt{35}$

$5\sqrt{7}$

$\sqrt{13}$

Correct answer:

$\sqrt{35}$

Explanation:

When dividing square roots, we divide the numbers inside the radical. Simplify if necessary.

$\frac{\sqrt{210}}{\sqrt{6}}=\frac{\sqrt{35}*\sqrt{6}}{\sqrt{6}}=\sqrt{35}$

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Example Question #2 : How To Divide Square Roots

Simplify: $\frac{\sqrt{432}}{\sqrt{36}}$

Possible Answers:

$2\sqrt{3}$

$3\sqrt{2}$

$6\sqrt{3}$

$\sqrt{12}$

Correct answer:

$2\sqrt{3}$

Explanation:

When dividing square roots, we divide the numbers inside the radical. Simplify if necessary.

$\frac{\sqrt{432}}{\sqrt{36}}=\frac{\sqrt{36}*\sqrt{12}}{\sqrt{36}}=\sqrt{12}$

Let's simplify this even further by factoring out a .

$\sqrt{12}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$

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Example Question #23 : Square Roots And Operations

Simplify: $\frac{\sqrt{1200}}{\sqrt{8}}$

Possible Answers:

$30\sqrt{5}$

$5\sqrt{30}$

$\sqrt{150}$

$6\sqrt{5}$

$5\sqrt{6}$

Correct answer:

$5\sqrt{6}$

Explanation:

When dividing square roots, we divide the numbers inside the radical. Simplify if necessary.

$\frac{\sqrt{1200}}{\sqrt{8}}=\frac{\sqrt{8}*\sqrt{150}}{\sqrt{8}}=\sqrt{150}$
Let's simplify this even further by factoring out a .

$\sqrt{150}=\sqrt{25}*\sqrt{6}=5\sqrt{6}$

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SAT Math : Square Roots and Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : Square Roots And Operations

Example Question #1 : How To Divide Square Roots

Example Question #91 : Arithmetic

Example Question #2 : How To Divide Square Roots

Example Question #23 : Square Roots And Operations

All SAT Math Resources

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