Square Roots and Cube Roots Questions and Answers

Q:

If 3a=4b=6c and $a + b + c = 27 \sqrt{29}$ , then $\sqrt{a^{2} + b^{2} + c^{2}} = ?$

A) 81	B) 83
C) 87	D) None of these

Answer & Explanation Answer: C) 87

Explanation:

$4 b = 6 c \Rightarrow b = \frac{3}{2} c a n d 3 a = 4 b \Rightarrow a = \frac{4}{3} b = \frac{4}{3} (\frac{3}{2} c) = 2 c$

$a + b + c = 27 \sqrt{29} \Rightarrow 2 c + \frac{3}{2} c + c = 27 \sqrt{29} \Rightarrow c = 6 \sqrt{29}$

$∴ \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{(a + b + b)^{2} - 2 (a b + b c + c a)}$

$= \sqrt{(27 \sqrt{29})^{2} - 2 (2 c \times \frac{3}{2} c + \frac{3}{2} c \times c + c \times 2 c)}$

$= \sqrt{(729 \times 29) - 2 \times \frac{13}{2} c^{2}}$

= 87

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Q:

If $\frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3} t h e n a & b = ?$

A) a=-11,b=-6	B) a=-11,b=6
C) a=11,b=-6	D) a=11,b=6

Answer & Explanation Answer: C) a=11,b=-6

Explanation:

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Q:

What is the number of decimal places in a cube root of a number having 27 decimal places ?

A) 3	B) 6
C) 9	D) 27

Answer & Explanation Answer: C) 9

Explanation:

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Q:

$\sqrt{(\frac{(0.75)^{3}}{1 - 0.75} + [0.75 + {(0.75)}^{2} + 1])} = ?$

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: B) 2

Explanation:

$\sqrt{(\frac{(0.75)^{3}}{1 - 0.75} + [0.75 + (0.75)^{2} + 1])} = \sqrt{\frac{(0.75)^{3} + (1 - 0.75) [(1)^{2} + (0.75)^{2} + 1 \times 0.75]}{1 - 0.75}}$

= $\sqrt{\frac{(0.75)^{3} + [(1)^{3} - (0.75)^{3}]}{1 - 0.75}} = \sqrt{\frac{1}{0.25}} = \sqrt{4} = 2$

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Q:

Find the value of $\sqrt{\frac{1.21 x 0.9}{1.1 x 0.11}}$ ?

A) 0	B) 1
C) 3	D) 5

Answer & Explanation Answer: C) 3

Explanation:

Given $\sqrt{\frac{1.21 x 0.9}{1.1 x 0.11}}$

= $\sqrt{\frac{1.21 x 100 x 0.9 x 10}{1.1 x 10 x 0.11 x 100}}$

= $\sqrt{9}$

= 3.

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Q:

$1 . 5^{2} x \sqrt{0.0225} = ?$

A) 0.0375	B) 0.3375
C) 3.275	D) 32.75

Answer & Explanation Answer: B) 0.3375

Explanation:

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Q:

The value of $\frac{\sqrt{80} - \sqrt{112}}{\sqrt{45} - \sqrt{63}}$ is:

A) 3/4	B) 4/3
C) 4/7	D) 7/4

Answer & Explanation Answer: B) 4/3

Explanation:

$\frac{\sqrt{80} - \sqrt{112}}{\sqrt{45} - \sqrt{63}} = \frac{\sqrt{16 \times 5} - \sqrt{16 \times 7}}{\sqrt{9 \times 5} - \sqrt{9 \times 7}} = \frac{4 \sqrt{5} - 4 \sqrt{7}}{3 \sqrt{5} - 3 \sqrt{7}}$

$= \frac{4 (\sqrt{5} - \sqrt{7})}{3 (\sqrt{5} - \sqrt{7})} = \frac{4}{3}$

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Q:

If $a = \frac{\sqrt{5} + 1}{\sqrt{5} - 1} b = \frac{\sqrt{5} - 1}{\sqrt{5} + 1} t h e n f i n d t h e v a l u e o f [\frac{a^{2} + a b + b^{2}}{a^{2} - a b + b^{2}}] i s : :$

A) 3/4	B) 4/3
C) 3/5	D) 5/3

Answer & Explanation Answer: B) 4/3

Explanation:

By simplifying, we get 4/3

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Square Roots and Cube Roots Questions

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