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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #44 : Basic Squaring / Square Roots

Simplify: $\sqrt{240}$

Possible Answers:

$4\sqrt{15}$

$15\sqrt2$

$5\sqrt{13}$

$12\sqrt{4}$

$3\sqrt{27}$

Correct answer:

$4\sqrt{15}$

Explanation:

Write out the common square factors of the number inside the square root.

$\sqrt{240}= \sqrt{4\times 60}= 2\sqrt{60}$

Continue to find the common factors for 60.

$2\sqrt{60} = 2\sqrt{4\times 15} = 2(2\sqrt{15}) = 4\sqrt{15}$

Since there are no square factors for $\sqrt{15}$ , the answer is in its simplified form. It might not have been easy to see that 16 was a common factor of 240.

The answer is: $4\sqrt{15}$

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Example Question #11 : How To Simplify Square Roots

Simplify:

$\sqrt{48}$

Possible Answers:

None of the given answers.

$2\sqrt{24}$

$4\sqrt{3}$

$3\sqrt{4}$

Correct answer:

$4\sqrt{3}$

Explanation:

To simplify, we want to find some factors of where at least one of the factors is a perfect square.

In this case, and are factors of , and is a perfect square.

We can simplify by saying:

$\sqrt{48} = \sqrt{16\cdot 3} = \sqrt{4^2 \cdot 3} = 4\sqrt{3}$

We could also recognize that two factors of are and . We could approach this way by saying:

$\sqrt{48}=\sqrt{4 \cdot 12} = \sqrt {2^2 \cdot 12} = 2\sqrt{12}$

But we wouldn't stop there. That's because can be further factored:

$2\sqrt{12} = 2\sqrt{4 \cdot 3} = 2\sqrt{2^2 \cdot 3} = 2\cdot 2 \sqrt{3} = 4\sqrt{3}$

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Example Question #51 : Basic Squaring / Square Roots

Simplify:

$\sqrt{20,000}$

Possible Answers:

None of the given answers.

$100\sqrt{2}$

$10\sqrt{2}$

$1000\sqrt{2}$

$10\sqrt{20}$

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 #51 : Basic Squaring / Square Roots

Simplify the following:

$2\sqrt{54}$

Possible Answers:

$4\sqrt{2}$

$6\sqrt{6}$

$4\sqrt{3}$

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 #52 : Basic Squaring / Square Roots

Simplify $\sqrt{88}$

Possible Answers:

$8\sqrt{11}$

$4\sqrt{22}$

$2\sqrt{22}$

$22\sqrt{2}$

$4\sqrt{11}$

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 : How To Simplify Square Roots

Simplify: $\sqrt{332}$

Possible Answers:

$4\sqrt{22}$

$16\sqrt{22}$

$4\sqrt{22}$

$16\sqrt{11}$

$8\sqrt{26}$

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 : How To Simplify Square Roots

Simplify: $8\sqrt{8}$

Possible Answers:

$12\sqrt{2}$

$24\sqrt{2}$

$16\sqrt{2}$

$10\sqrt{2}$

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 : How To Simplify Square Roots

Simplify: $5\sqrt{98}$

Possible Answers:

$35\sqrt{2}$

$12\sqrt{5}$

$15\sqrt{7}$

$12\sqrt{2}$

$17\sqrt{2}$

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 : How To Simplify Square Roots

Simplify: $\sqrt{1200}$

Possible Answers:

$20\sqrt{30}$

$20\sqrt{3}$

$16\sqrt{15}$

$400\sqrt{3}$

$40\sqrt{3}$

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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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #44 : Basic Squaring / Square Roots

Example Question #11 : How To Simplify Square Roots

Example Question #51 : Basic Squaring / Square Roots

Example Question #13 : Simplifying Square Roots

Example Question #51 : Basic Squaring / Square Roots

Example Question #52 : Basic Squaring / Square Roots

Example Question #23 : How To Simplify Square Roots

Example Question #24 : How To Simplify Square Roots

Example Question #25 : How To Simplify Square Roots

Example Question #26 : How To Simplify Square Roots

All SAT Math Resources

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