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SSAT Middle Level Math : Squares / Square Roots

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

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Example Questions

Example Question #1 : Squares / Square Roots

Evaluate: $\sqrt{100} + \sqrt{49 } - \sqrt{36}$

Possible Answers:

Correct answer:

Explanation:

Find the individual square roots and perform the operations on them.

$\sqrt{100} = 10$

$\sqrt{49 } = 7$

$\sqrt{36} = 6$

$\sqrt{100} + \sqrt{49 } - \sqrt{36} = 10 + 7 - 6 = 17-6 = 11$

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Example Question #2 : Squares / Square Roots

The square root of a number is 43. What is that number?

Possible Answers:

1,809

1,869

1,849

1,729

1,789

Correct answer:

1,849

Explanation:

By definition, the square root of a number multiplied by itself yields that number. Therefore, 43 is the square root of $43 \cdot 43 = 1,849$ .

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Example Question #3 : Squares / Square Roots

The square root of a number is 58. What is that number?

Possible Answers:

3,364

3,264

3,024

3,524

3,424

Correct answer:

3,364

Explanation:

By definition, the square root of a number multiplied by itself yields that number. Therefore,

$58 \cdot 58 = 3,364$ .

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Example Question #4 : How To Find The Square Root

$\frac{\sqrt{64}-\sqrt{36}}{\sqrt{4}}=$

Possible Answers:

Correct answer:

Explanation:

First, find the square root of each number:

$\sqrt{64}=8$

$\sqrt{36}=6$

$\sqrt{4}=2$

Then, solve the equation accordingly.

$\frac{8-2}{2}=$

$\frac{2}{2}=1$

The answer is

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Example Question #1 : Squares / Square Roots

Evaluate: $\sqrt{121}$

Possible Answers:

Correct answer:

Explanation:

The square root of a number is the number which, when multiplied by itself, yields that number. Since $11 \cdot 11 = 121$ , $\sqrt{121} = 11$ .

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Example Question #4 : Squares / Square Roots

Which of the following statements is true about $\sqrt{441}$ ?

Possible Answers:

$20 < \sqrt{441} < 21$

$19 < \sqrt{441} < 20$

$\sqrt{441} = 19$

$21 < \sqrt{441} < 22$

$\sqrt{441} = 21$

Correct answer:

$\sqrt{441} = 21$

Explanation:

The square root of a number is the number which, when multiplied by itself, yields that number. Since $21 \cdot 21 = 441$ , $\sqrt{441} = 21$ .

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Example Question #5 : Squares / Square Roots

Which of the following statements is true about $\sqrt{ 231}$ ?

Possible Answers:

$15 <\sqrt{ 231} < 16$

$17 <\sqrt{ 231} < 18$

$\sqrt{ 231} = 17$

$\sqrt{ 231} = 19$

$16 <\sqrt{ 231} < 17$

Correct answer:

$15 <\sqrt{ 231} < 16$

Explanation:

The square root of a number is the number which, when multiplied by itself, yields that number. Since $15 \cdot 15 = 225$ , $16 \cdot 16 = 256$ , and

$15^{2} = 225 < 231 < 256 = 16^{2}$

then

$15 = \sqrt{225 }< 231 <\sqrt{ 256} = 16$

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Example Question #8 : How To Find The Square Root

Evaluate:

$\sqrt{169}$

Possible Answers:

Correct answer:

Explanation:

The square root of a number is the number which, when multiplied by itself, yields that number. Since $13 \cdot 13 = 169$ , $\sqrt{169} = 13$ .

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Example Question #9 : How To Find The Square Root

Which of the following statements is true about $\sqrt{-225}$ ?

Possible Answers:

$\sqrt{-225}$ is undefined in the set of real numbers.

$-17 < \sqrt{-225} < -16$

$-15 < \sqrt{-225} < -14$

$-16 < \sqrt{-225} < -15$

$\sqrt{-225} = -15$

Correct answer:

$\sqrt{-225}$ is undefined in the set of real numbers.

Explanation:

A negative number does not have a real square root, so this is the correct choice.

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Example Question #6 : Squares / Square Roots

A square has an area of $16\ ft^{2}$ .

How long is each of its sides?

Possible Answers:

Correct answer:

Explanation:

The two sides of the square must be the same length, and multiply to give 16. So we are looking for the $\sqrt{16}$ which is .

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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 #1 : Squares / Square Roots

Example Question #2 : Squares / Square Roots

Example Question #3 : Squares / Square Roots

Example Question #4 : How To Find The Square Root

Example Question #1 : Squares / Square Roots

Example Question #4 : Squares / Square Roots

Example Question #5 : Squares / Square Roots

Example Question #8 : How To Find The Square Root

Example Question #9 : How To Find The Square Root

Example Question #6 : Squares / Square Roots

All SSAT Middle Level Math Resources

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