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SAT Math : Arithmetic

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Example Questions

Example Question #11 : Simplifying Square Roots

Simplify:

$\sqrt{20,000}$

Possible Answers:

$1000\sqrt{2}$

$10\sqrt{20}$

None of the given answers.

$10\sqrt{2}$

$100\sqrt{2}$

Correct answer:

$100\sqrt{2}$

Explanation:

To simplify, we want to find factors of 20,000 where at least one is a perfect square. With this in mind, we find that:

$\sqrt{20,000} = \sqrt{2 \cdot 10,000} = \sqrt{2 \cdot 100^2} = 100\sqrt{2}$

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Example Question #13 : Simplifying Square Roots

Simplify and add:

$\sqrt {64}+\sqrt {27}-\sqrt {81}+\sqrt {3}$ . (Only positive integers)

Possible Answers:

$-4\sqrt{3}-1$

$4\sqrt{3}+1$

$4\sqrt {3}-1$

None of the Above

Correct answer:

$4\sqrt {3}-1$

Explanation:

Step 1: We need to simplify all the roots:

$\sqrt{64}=\sqrt{16}\cdot\sqrt{4}=4\cdot2=8$

$\sqrt {27}=\sqrt {9}\cdot\sqrt {3}=3\cdot\sqrt{3}=3\sqrt{3}$

$\sqrt {81}=\sqrt{9}\cdot\sqrt{9}=3*3=9$

$\sqrt{3}\rightarrow\sqrt{3}$ (I am not changing this one, it's already simplified)

Step 2: Rewrite the problem with the simplified parts we found in step 1

$8+3\sqrt{3}-9+\sqrt{3}$

Step 3: Combine Like terms:

Numbers: 8-9=-1

Roots: $3\sqrt{3}+\sqrt{3}=4\sqrt{3}$

Step 4: Write the final answer. It does not matter how you write it.

$4\sqrt{3}-1$

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Example Question #21 : Simplifying Square Roots

Simplify the following:

$2\sqrt{54}$

Possible Answers:

$4\sqrt{2}$

$4\sqrt{3}$

$6\sqrt{6}$

Correct answer:

$6\sqrt{6}$

Explanation:

To solve, you must first break up 54 into its smallest prime factors. Those are:

54=2*27=2*9*3

Since our root has index 2, that means that for every 2 identical factors inside, you can pull 1 out. Thus, we get

$2*3\sqrt{2*3}=6\sqrt6$

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Example Question #22 : Simplifying Square Roots

Simplify $\sqrt{88}$

Possible Answers:

$4\sqrt{22}$

$22\sqrt{2}$

$2\sqrt{22}$

$4\sqrt{11}$

$8\sqrt{11}$

Correct answer:

$2\sqrt{22}$

Explanation:

To simplify a square root, we need to find perfect squares. In this case, it is .

$\sqrt{88}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$

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Example Question #23 : Simplifying Square Roots

Simplify: $\sqrt{332}$

Possible Answers:

$4\sqrt{22}$

$16\sqrt{22}$

$16\sqrt{11}$

$4\sqrt{22}$

$8\sqrt{26}$

Correct answer:

$4\sqrt{22}$

Explanation:

To simplify a square root, we need to find perfect squares. In this case, it is .

$\sqrt{332}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$

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Example Question #24 : Simplifying Square Roots

Simplify: $8\sqrt{8}$

Possible Answers:

$10\sqrt{2}$

$16\sqrt{2}$

$12\sqrt{2}$

$24\sqrt{2}$

Correct answer:

$16\sqrt{2}$

Explanation:

To simplify a square root, we need to find perfect squares. In this case, it is . Since there is a number outside the radical, we ignore that for now and later we multiply the number and square root.

$8\sqrt{8}=8*\sqrt{4}*\sqrt{2}=8*2*\sqrt{2}=16\sqrt{2}$

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Example Question #25 : Simplifying Square Roots

Simplify: $5\sqrt{98}$

Possible Answers:

$17\sqrt{2}$

$12\sqrt{2}$

$15\sqrt{7}$

$12\sqrt{5}$

$35\sqrt{2}$

Correct answer:

$35\sqrt{2}$

Explanation:

To simplify a square root, we need to find perfect squares. In this case, it is . Since there is a number outside the radical, we ignore that for now and later we multiply the number and square root.

$5\sqrt{98}=5*\sqrt{49}8\sqrt{2}=5*7*\sqrt{2}=35\sqrt{2}$

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Example Question #26 : Simplifying Square Roots

Simplify: $\sqrt{1200}$

Possible Answers:

$20\sqrt{30}$

$40\sqrt{3}$

$400\sqrt{3}$

$20\sqrt{3}$

$16\sqrt{15}$

Correct answer:

$20\sqrt{3}$

Explanation:

To simplify radicals, we need to find a perfect square to factor out. In this case, its 400 .

$\sqrt{1200}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$

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Example Question #27 : Simplifying Square Roots

Simplify: $\sqrt{375}$

Possible Answers:

$3\sqrt{55}$

$5\sqrt{30}$

$25\sqrt{15}$

$15\sqrt{5}$

$5\sqrt{15}$

Correct answer:

$5\sqrt{15}$

Explanation:

To simplify radicals, we need to find a perfect square to factor out. In this case, its .

$\sqrt{375}=\sqrt{25}*\sqrt{15}=5\sqrt{15}$

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Example Question #28 : Simplifying Square Roots

Simplify: $\sqrt{x^5}$

Possible Answers:

$x^2\sqrt{x^3}$

$x^2\sqrt{x}$

$2x\sqrt{x}$

$x\sqrt{x}$

$x\sqrt{x^3}$

Correct answer:

$x^2\sqrt{x}$

Explanation:

To solve this, we know perfect squares are able to simplify easily to the base it is. Let's find all the perfect squares in x^5 .

$\sqrt{x^5}=\sqrt{x^2}*\sqrt{x^2}*\sqrt{x}=x*x\sqrt{x}=x^2\sqrt{x}$

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SAT Math : Arithmetic

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : Simplifying Square Roots

Example Question #13 : Simplifying Square Roots

Example Question #21 : Simplifying Square Roots

Example Question #22 : Simplifying Square Roots

Example Question #23 : Simplifying Square Roots

Example Question #24 : Simplifying Square Roots

Example Question #25 : Simplifying Square Roots

Example Question #26 : Simplifying Square Roots

Example Question #27 : Simplifying Square Roots

Example Question #28 : Simplifying Square Roots

All SAT Math Resources

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