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

Possible Answers:

$\displaystyle 15$

$\displaystyle 11$

$\displaystyle 23$

$\displaystyle 18$

$\displaystyle 13$

Correct answer:

$\displaystyle 11$

Explanation:

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

$\sqrt{100} = 10$ $\displaystyle \sqrt{100} = 10$

$\sqrt{49 } = 7$ $\displaystyle \sqrt{49 } = 7$

$\sqrt{36} = 6$ $\displaystyle \sqrt{36} = 6$

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

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Example Question #1 : How To Find The Square Root

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

Possible Answers:

1,789 $\displaystyle 1,789$

1,869 $\displaystyle 1,869$

1,729 $\displaystyle 1,729$

1,809 $\displaystyle 1,809$

1,849 $\displaystyle 1,849$

Correct answer:

1,849 $\displaystyle 1,849$

Explanation:

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

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Example Question #3 : How To Find The Square Root

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

Possible Answers:

3,024 $\displaystyle 3,024$

3,364 $\displaystyle 3,364$

3,424 $\displaystyle 3,424$

3,264 $\displaystyle 3,264$

3,524 $\displaystyle 3,524$

Correct answer:

3,364 $\displaystyle 3,364$

Explanation:

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

$58 \cdot 58 = 3,364$ $\displaystyle 58 \cdot 58 = 3,364$ .

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Example Question #2 : Squares / Square Roots

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

Possible Answers:

$\displaystyle 1$

$\displaystyle 4$

$\displaystyle 3$

$\displaystyle 2$

Correct answer:

$\displaystyle 1$

Explanation:

First, find the square root of each number:

$\sqrt{64}=8$ $\displaystyle \sqrt{64}=8$

$\sqrt{36}=6$ $\displaystyle \sqrt{36}=6$

$\sqrt{4}=2$ $\displaystyle \sqrt{4}=2$

Then, solve the equation accordingly.

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

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

The answer is $\displaystyle 1.$

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Example Question #2 : How To Find The Square Root

Evaluate: $\sqrt{121}$ $\displaystyle \sqrt{121}$

Possible Answers:

$\displaystyle 13$

$\displaystyle 7$

$\displaystyle 9$

$\displaystyle 11$

$\displaystyle 17$

Correct answer:

$\displaystyle 11$

Explanation:

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

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Example Question #6 : How To Find The Square Root

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

Possible Answers:

$19 < \sqrt{441} < 20$ $\displaystyle 19 < \sqrt{441} < 20$

$\sqrt{441} = 21$ $\displaystyle \sqrt{441} = 21$

$\sqrt{441} = 19$ $\displaystyle \sqrt{441} = 19$

$20 < \sqrt{441} < 21$ $\displaystyle 20 < \sqrt{441} < 21$

$21 < \sqrt{441} < 22$ $\displaystyle 21 < \sqrt{441} < 22$

Correct answer:

$\sqrt{441} = 21$ $\displaystyle \sqrt{441} = 21$

Explanation:

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

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Example Question #2 : How To Find The Square Root

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

Possible Answers:

$15 <\sqrt{ 231} < 16$ $\displaystyle 15 < \sqrt{ 231} < 16$

$\sqrt{ 231} = 17$ $\displaystyle \sqrt{ 231} = 17$

$16 <\sqrt{ 231} < 17$ $\displaystyle 16 < \sqrt{ 231} < 17$

$17 <\sqrt{ 231} < 18$ $\displaystyle 17 < \sqrt{ 231} < 18$

$\sqrt{ 231} = 19$ $\displaystyle \sqrt{ 231} = 19$

Correct answer:

$15 <\sqrt{ 231} < 16$ $\displaystyle 15 < \sqrt{ 231} < 16$

Explanation:

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

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

then

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

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Example Question #3 : How To Find The Square Root

Evaluate:

$\sqrt{169}$ $\displaystyle \sqrt{169}$

Possible Answers:

$\displaystyle 7$

$\displaystyle 17$

$\displaystyle 9$

$\displaystyle 13$

$\displaystyle 11$

Correct answer:

$\displaystyle 13$

Explanation:

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

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Example Question #9 : How To Find The Square Root

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

Possible Answers:

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

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

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

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

$\sqrt{-225} = -15$ $\displaystyle \sqrt{-225} = -15$

Correct answer:

$\sqrt{-225}$ $\displaystyle \sqrt{-225}$ 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 #10 : How To Find The Square Root

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

How long is each of its sides?

Possible Answers:

$\displaystyle 9$

$\displaystyle 3$

$\displaystyle 12$

$\displaystyle 4$

$\displaystyle 8$

Correct answer:

$\displaystyle 4$

Explanation:

The two sides of the square must be the same length, and multiply to give 16. So we are looking for the $\sqrt{16}$ $\displaystyle \sqrt{16}$ which is $\displaystyle 4$ .

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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 #1 : How To Find The Square Root

Example Question #3 : How To Find The Square Root

Example Question #2 : Squares / Square Roots

Example Question #2 : How To Find The Square Root

Example Question #6 : How To Find The Square Root

Example Question #2 : How To Find The Square Root

Example Question #3 : How To Find The Square Root

Example Question #9 : How To Find The Square Root

Example Question #10 : How To Find The Square Root

All SSAT Middle Level Math Resources

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