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ISEE Middle Level Quantitative : Squares / Square Roots

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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All ISEE Middle Level Quantitative Resources

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Example Questions

Example Question #1 : Squares / Square Roots

Give the square root of 256.

Possible Answers:

Correct answer:

Explanation:

$16\cdot16= 256$ - that is, 16 squared is 256, making 16 the square root of 256 by definition.

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Example Question #1 : Squares / Square Roots

Which is the greater quantity?

(a) $\sqrt{425 }$

(b)

Possible Answers:

(a) and (b) are equal

(b) is greater

(a) is greater

It is impossible to tell from the information given

Correct answer:

(b) is greater

Explanation:

$21^{2} = 21 \times 21 = 441$ , so $21 = \sqrt{441}$

441 > 425 , so

$21 = \sqrt{441} > \sqrt{425}$

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Example Question #2 : Squares / Square Roots

Which is the greater quantity?

(a) $6 \sqrt{ 7}$

(b) $7 \sqrt{6}$

Possible Answers:

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

Correct answer:

(b) is greater

Explanation:

(a) $\left (6 \sqrt{7} \right )^{2} = 6^{2}\left ( \sqrt{7} \right ) ^{2} = 36 \cdot 7 = 252$ , so $6 \sqrt{7} = \sqrt{ 252 }$

(b) $\left (7 \sqrt{6} \right )^{2} = 7^{2}\left ( \sqrt{6} \right ) ^{2} = 49 \cdot 6 = 294$ , so $7\sqrt{6} = \sqrt{ 294 }$

294 > 252 ,

$\sqrt{294 }> \sqrt{252}$ ,

and

$7\sqrt{6} > 6 \sqrt{7}$

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Example Question #3 : How To Find The Square Root

Column A Column B

$\sqrt{100}$ $\sqrt{10.0}$

Possible Answers:

The quantity in Column A is greater.

The quantities are equal.

The quantity in Column B is greater.

There is no relationship between the quantities.

Correct answer:

The quantity in Column A is greater.

Explanation:

The square root of 100 is 10, while the square root of 10 is between the square root of 9 and 16, so about 4. Therefore, Column A has to be greater.

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Example Question #4 : How To Find The Square Root

Which of the following is equal to $\sqrt{5^{2}+7^{2}+7}$ ?

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

$\sqrt{5^{2}+7^{2}+7}$

$=\sqrt{25 +49+7}$

$=\sqrt{81}$

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Example Question #1 : Squares / Square Roots

Which of the following is equal to $\sqrt{11^{2}+ 6 \cdot 8}$ ?

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

$\sqrt{11^{2}+ 6 \cdot 8}$

$= \sqrt{121+ 6 \cdot 8}$

$= \sqrt{121+ 48}$

$= \sqrt{169}$

=13

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Example Question #2 : Squares / Square Roots

Which of the following is equal to $\sqrt{2^{3}+ 6^{2}+10^{2}}$ ?

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

$\sqrt{2^{3}+ 6^{2}+10^{2}}$

$=\sqrt{8+36 +100}$

$=\sqrt{ 144}$

=12

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Example Question #6 : How To Find The Square Root

$V^{2} = 72$ ; is positive.

Which is the greater quantity?

(a)

(b)

Possible Answers:

(A) and (B) are equal

(B) is greater

It is impossible to tell which is greater from the information given

(A) is greater

Correct answer:

(A) is greater

Explanation:

Since is positive, we can compare to 8 by comparing their squares.

$V^{2} = 72$ and $8^{2} = 8 \times 8 = 64$

$V^{2} > 8^{2}$ , so V>8 , making (A) greater.

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Example Question #6 : How To Find The Square Root

$F^{2}= 36$

Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) is greater

It is impossible to tell which is greater from the information given

(B) is greater

(A) and (B) are equal

Correct answer:

It is impossible to tell which is greater from the information given

Explanation:

If $F^{2} = 36$ , then one of two things is true - either F = 6 or F = -6 .

However, 6 > 4 and -6<4 , so it is impossibe to tell whether (A) or (B) is greater.

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Example Question #7 : How To Find The Square Root

$Q^{2} = 49$

Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) and (B) are equal

(A) is greater

(B) is greater

It is impossible to tell which is greater from the information given

Correct answer:

(A) is greater

Explanation:

If $Q^{2} = 49$ , then one of two things is true - either Q=7 or Q=- 7 . Since 7 > -8 and -7 > -8 , Q > -8 either way, so (A) is greater.

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : Squares / Square Roots

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #1 : Squares / Square Roots

Example Question #1 : Squares / Square Roots

Example Question #2 : Squares / Square Roots

Example Question #3 : How To Find The Square Root

Example Question #4 : How To Find The Square Root

Example Question #1 : Squares / Square Roots

Example Question #2 : Squares / Square Roots

Example Question #6 : How To Find The Square Root

Example Question #6 : How To Find The Square Root

Example Question #7 : How To Find The Square Root

All ISEE Middle Level Quantitative Resources

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