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ISEE Middle Level Quantitative : How to find the square root

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

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Example Question #11 : How To Find The Square Root

Which is the greater quantity?

(A) $\sqrt{9} + \sqrt{25}$

(B) $\sqrt{34}$

Possible Answers:

(A) and (B) are equal

(B) is greater

(A) is greater

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

Correct answer:

(A) is greater

Explanation:

$\sqrt{9} + \sqrt{25} = 3 + 5 = 8$

since $8^{2} = 8 \times 8 = 64$ , $8 = \sqrt{64}$ .

Since 64 > 34 , $\sqrt{64} > \sqrt{34}$ , and (A) is greater

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Example Question #12 : How To Find The Square Root

Which is the greater quantity?

(A) $\sqrt{4 \cdot 9 \cdot 25}$

(B) $2 \cdot 3 \cdot 5$

Possible Answers:

(A) is greater

(B) is greater

(A) and (B) are equal

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

Correct answer:

(A) and (B) are equal

Explanation:

$\sqrt{4 \cdot 9 \cdot 25} = \sqrt{900} = 30$

$2 \cdot 3 \cdot 5 = 30$

The quantities are equal.

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Example Question #13 : How To Find The Square Root

Which is the greater quantity?

(A)

(B) $\sqrt{600}$

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:

$25 ^{2} = 25 \times 25 = 625$ , so

$25 = \sqrt{625} > \sqrt{600}$

This makes (A) greater.

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Example Question #14 : How To Find The Square Root

Which is the greater quantity?

(A) $\sqrt{100^{4}}$

(B) $100^{2}$

Possible Answers:

(A) is greater

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

(A) and (B) are equal

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

$\sqrt{100^{4}} = \sqrt{100 \times 100 \times 100 \times 100} = \sqrt{100,000,000} = 10,000$

$100^{2} = 100 \times 100 = 10,000$

The quantities are equal.

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Example Question #15 : How To Find The Square Root

Which of the following is equal to $\sqrt{4 \cdot 9 \cdot 16}$ ?

Possible Answers:

Correct answer:

Explanation:

First, simplify the terms within the square root by multiplying.

$\sqrt{4 \cdot 9 \cdot 16} = \sqrt{36 \cdot 16} = \sqrt{576}$

Then, solve the sqaure root.

$\sqrt{576}=24$

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Example Question #16 : How To Find The Square Root

Which of the following is equal to $\sqrt{4^{2} \cdot 3^{2}}$ ?

Possible Answers:

Correct answer:

Explanation:

First, evalutate the terms under the radical:

$\sqrt{4^{2} \cdot 3^{2}} = \sqrt{16 \cdot 9} =\sqrt{144}$

Then, take the square root:

$\sqrt{144}=12$

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Example Question #17 : Squares / Square Roots

Which is the greater quantity?

(A) $\sqrt{1+ 4+ 9 + 16 + 25 + 36}$

(B)

Possible Answers:

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

(A) and (B) are equal

(B) is greater

(A) is greater

Correct answer:

(A) is greater

Explanation:

1+ 4+ 9 + 16 + 25 + 36

=5 + 9 + 16 + 25 + 36

=14 + 16 + 25 + 36

=30+ 25 + 36

=55 + 36

=91

Therefore, $\sqrt{1+ 4+ 9 + 16 + 25 + 36} = \sqrt{91}$ .

Since $9^{2} = 9 \times 9 = 81$ , $9 = \sqrt{81}$ .

91 > 81 , so $\sqrt{91 }>\sqrt{ 81}$ , and (A) is greater.

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Example Question #17 : How To Find The Square Root

Which of the following is equal to 39?

Possible Answers:

$12\cdot3+6$

$16\cdot3+3$

$12\cdot3+3$

$12\cdot2+3$

Correct answer:

$12\cdot3+3$

Explanation:

$12\cdot3+3$ is equal to:

36+3

Therefore, $12\cdot3+3$ is the correct answer.

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Example Question #19 : Squares / Square Roots

is a positive integer; is a negative integer; A +B =1 .

Which is the greater quantity?

(a) $\sqrt{A^{2}}$

(b) $\sqrt{B^{2}}$

Possible Answers:

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

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

(a) is the greater quantity

Explanation:

A +B =1 , then B = 1-A . Since is negative, let be the opposite of . Therefore, C= - B = - ( 1-A) =A-1 .

Two numbers that are each other's opposite have the same square, so

$C^{2} = B^{2}$

C = A-1 < A , so, since and are positive,

$C^{2} < A^{2}$

By substitution,

$B^{2}< A^{2}$ ,

and

$\sqrt{B^{2}}<\sqrt{ A^{2}}$ .

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Example Question #20 : Squares / Square Roots

is a positive integer; A B =0 . Which is the greater quantity?

(a) $\sqrt{A}$

(b) $\sqrt{B}$

Possible Answers:

(b) is the greater quantity

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

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

(a) is the greater quantity

Explanation:

If A B =0 , then by the zero product principle, one or both of and is equal to 0. Since is positive, B = 0 . Also, since is positive, $\sqrt{A}$ is positive, and $\sqrt{B } = \sqrt{0}= 0$ . Thus, $\sqrt{A} >\sqrt{B }$ .

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ISEE Middle Level Quantitative : How to find the square root

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #11 : How To Find The Square Root

Example Question #12 : How To Find The Square Root

Example Question #13 : How To Find The Square Root

Example Question #14 : How To Find The Square Root

Example Question #15 : How To Find The Square Root

Example Question #16 : How To Find The Square Root

Example Question #17 : Squares / Square Roots

Example Question #17 : How To Find The Square Root

Example Question #19 : Squares / Square Roots

Example Question #20 : Squares / Square Roots

All ISEE Middle Level Quantitative Resources

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