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SSAT Middle Level Math : Squares / Square Roots

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Example Questions

Example Question #11 : Squares / Square Roots

Evaluate:

$\sqrt{121} + \sqrt{49}$

Possible Answers:

Correct answer:

Explanation:

$11 ^{2 } = 11 \times 11 = 121$ , so $\sqrt{121} = 11$ .

$7 ^{2 } = 7 \times 7 = 49$ , so $\sqrt{49} = 7$ .

$\sqrt{121} + \sqrt{49} = 11 + 7 = 18$

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Example Question #12 : How To Find The Square Root

Let $N = \sqrt{7^{2}-5^{2}-3^{2}}$

Then which of the following statements is correct?

Possible Answers:

3 < N < 4

N = 3

2< N <3

N = 2

1< N <2

Correct answer:

3 < N < 4

Explanation:

$N = \sqrt{7^{2}-5^{2}-3^{2}} = \sqrt{49-25-9} = \sqrt{24-9} = \sqrt{15}$

9 < 15 < 16 , so

$\sqrt{9} < \sqrt{15} < \sqrt{16}$

3 < N < 4

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Example Question #12 : Squares / Square Roots

Let $N = \sqrt{10 \times 20 + 7 \times 8}$

Which of the following is a true statement?

Possible Answers:

14 <N< 15

N = 16

N = 14

15 <N< 16

N = 15

Correct answer:

N = 16

Explanation:

$N = \sqrt{10 \times 20 + 7 \times 8}= \sqrt{200 + 56}= \sqrt{256}$

Since 16^2 = 256 , $N = \sqrt{256} = 16$

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Example Question #11 : How To Find The Square Root

Which of the answer choices is equivalent to $2\sqrt{3}$ ?

Possible Answers:

$\sqrt{36}$

$\sqrt{6}$

$\sqrt{18}$

$\sqrt{12}$

$\sqrt{9}$

Correct answer:

$\sqrt{12}$

Explanation:

can also be written as $\sqrt{4}$ , so $2\sqrt{3}$ can also be written as $\sqrt{4\cdot 3}$ , or $\sqrt{12}$ .

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Example Question #13 : Squares / Square Roots

What is the square root of ?

Possible Answers:

2401

Correct answer:

Explanation:

The square root of is , since $7\cdot7=49$ .

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Example Question #16 : How To Find The Square Root

Which of the answer choices is equivalent to $\sqrt{24}$ ?

Possible Answers:

$2\sqrt{6}$

$2\sqrt{4}$

Correct answer:

$2\sqrt{6}$

Explanation:

Recognize that $\sqrt{24}=\sqrt{4\cdot 6}$ . Since $\sqrt{4}=2$ , we can move the outside of the radical sign. This leaves us with $2\sqrt{6}$ .

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Example Question #2121 : Ssat Middle Level Quantitative (Math)

$x^{2} = 49, \left | x\right | + 7 = ?$

Possible Answers:

Correct answer:

Explanation:

If $x^{2} = 49$ , then $x=\pm 7$ .

$\left | 7 \right |=7,\ \left | -7 \right |=7$

Therefore, $\left | x \right |+7=7+7=14$ .

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Example Question #2121 : Ssat Middle Level Quantitative (Math)

Evaluate:

$\sqrt{\frac{169}{100}}$

Possible Answers:

$\frac{13}{10}$

$\frac{10}{13}$

$-\frac{13}{10}$

$\sqrt{\frac{169}{100}}$ is undefined.

$-\frac{10}{13}$

Correct answer:

$\frac{13}{10}$

Explanation:

To find the square root of a fraction, extract the square root of both the numerator and the denominator. Since $10 ^{2} = 10 \times 10 = 100$ , $\sqrt{100} = 10$ , and since $13^{2} = 169$ , $\sqrt{169} = 13$ .

Combine these results:

$\sqrt{\frac{169}{100}} = \frac{\sqrt{169}}{\sqrt{100}} = \frac{13}{10}$

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Example Question #13 : How To Find The Square Root

Evaluate:

$\sqrt{0.0009}$

Possible Answers:

0.0003

0.003

$\sqrt{0.0009}$ is an undefined quantity.

0.03

0.00003

Correct answer:

0.03

Explanation:

$0.0009= \frac{9}{10,000}$ , so

$\sqrt{0.0009} = \sqrt{\frac{9}{10,000}}$ .

The square root of a fraction can be determined by taking the square roots of both numerator and denominator. Since $3^{2} = 9$ , $\sqrt{9 } = 3$ , and since $100^{2} = 10,000$ , $\sqrt{10,000} = 100$ . Therefore,

$\sqrt{0.0009} = \sqrt{\frac{9}{10,000}} = \frac{\sqrt{9}}{\sqrt{10,000}} = \frac{3}{100} = 0.03$ .

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Example Question #20 : How To Find The Square Root

Note: The square root of a number is the number times itself. For example the square root of 4 is 2 because 2 x 2 = 4 or 2 squared is 4.

Find the square root of

$\sqrt{144}$ .

Possible Answers:

$4^{2} \times 3^{2}$

$12^{2}$

Correct answer:

Explanation:

So we are looking for a number that when it is squared is equal to 144. At this point you have to take some guesses.

$10^{2}=100$

$11^{2}=121$

Your getting closer

$13^{2}=169$

So it must be between 11 and 13, lets try 12.

$12^{2}=144$

So 12 is the answer.

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All SSAT Middle Level Math Resources

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SSAT Middle Level Math : Squares / Square Roots

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #11 : Squares / Square Roots

Example Question #12 : How To Find The Square Root

Example Question #12 : Squares / Square Roots

Example Question #11 : How To Find The Square Root

Example Question #13 : Squares / Square Roots

Example Question #16 : How To Find The Square Root

Example Question #2121 : Ssat Middle Level Quantitative (Math)

Example Question #2121 : Ssat Middle Level Quantitative (Math)

Example Question #13 : How To Find The Square Root

Example Question #20 : How To Find The Square Root

All SSAT Middle Level Math Resources

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