Square Roots and Cube Roots Questions and Answers

Q:

The cube root of .000216 is:

A) .6	B) .06
C) 77	D) 87

Answer & Explanation Answer: B) .06

Explanation:

${(. 000216)}^{\frac{1}{3}} = {(\frac{216}{10^{6}})}^{\frac{1}{3}} = {[\frac{6 * 6 * 6}{10^{2} * 10^{2} * 10^{2}}]}^{\frac{1}{3}} = [\frac{6}{10^{2}}] = 0.06$

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Q:

If x = $7 - 4 \sqrt{3} t h e n f i n d t h e v a l u e o f (x + \frac{1}{x}) ?$

A) 3sqrt{3}	B) 8sqrt{3}
C) 14	D) 14+8sqrt{3}

Answer & Explanation Answer: C) 14

Explanation:

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Q:

If $\sqrt{0.00000676} = 0.0026$ then $\sqrt{6760000}$ is:

A) 2.6	B) 26
C) 260	D) 2600

Answer & Explanation Answer: D) 2600

Explanation:

$\sqrt{6760000} = \sqrt{0.00000676 \times 10^{2}} = \sqrt{0.00000676} \times \sqrt{10^{2}} = 0.0026 \times 10^{6} = 2600$

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Q:

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

A) 57	B) 67
C) 77	D) 87

Answer & Explanation Answer: C) 77

Explanation:

Money collected = (59.29 x 100) paise = 5929 paise.

Number of members = $\sqrt{5929}$ = 77.

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Q:

The value of $\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225}}}}}$ is:

A) 4	B) 6
C) 8	D) 10

Answer & Explanation Answer: A) 4

Explanation:

$\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225}}}}} \sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + 15}}}} \sqrt{10 + \sqrt{25 + \sqrt{108 + 13}}} \sqrt{10 + \sqrt{25 + 11}} \sqrt{10 + 6} \sqrt{16} = 4$

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Q:

If $\sqrt{18225} = 135$ , then the value of $(\sqrt{182.25} + \sqrt{1.8225} + \sqrt{0.018225} + \sqrt{0.00018225})$ is:

A) 1.49985	B) 14.9985
C) 149.985	D) 1499.85

Answer & Explanation Answer: B) 14.9985

Explanation:

Given exp = $\sqrt{\frac{18225}{10^{2}}} + \sqrt{\frac{18225}{10^{4}}} + \sqrt{\frac{18225}{10^{6}}} + \sqrt{\frac{18225}{10^{8}}}$

= $\frac{\sqrt{18225}}{10} + \frac{\sqrt{18225}}{10^{2}} + \frac{\sqrt{18225}}{10^{3}} + \frac{\sqrt{18225}}{10^{4}}$

= $\frac{135}{10} + \frac{135}{100} + \frac{135}{1000} + \frac{135}{10000}$

= 13.5+1.35+0.135+0.0135=14.9985

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Q:

$\frac{3 + \sqrt{6}}{5 \sqrt{3} - 2 \sqrt{12} - \sqrt{30} + \sqrt{50}} = ?$

A) 3	B) 3sqrt{2}
C) 6	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

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Q:

What should come in place of both the question marks in the equation

$\frac{?}{\sqrt{128}} = \frac{\sqrt{162}}{?}$

A) 12	B) 14
C) 144	D) 196

Answer & Explanation Answer: A) 12

Explanation:

Let $\frac{x}{\sqrt{128}} = \frac{\sqrt{162}}{x}$

Then, $x^{2} = \sqrt{128 \times 162} = \sqrt{64 \times 2 \times 18 \times 9} = \sqrt{(8^{2} \times 6^{2} \times 3^{2})} = 8 \times 6 \times 3 = 144$

$∴ x = 12$

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