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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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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:

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:

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

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:

$\sqrt{\frac{0.204 \times 42}{0.07 \times 3.4}}$ is equal to:

A) 1/6	B) 0.06
C) 0.6	D) 6

Answer & Explanation Answer: D) 6

Explanation:

$\sqrt{\frac{0.204 \times 42}{0.07 \times 3.4}} = \sqrt{\frac{8568}{238}} = \sqrt{36} = 6$

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Q:

If $3 \sqrt{5} + \sqrt{125} = 17.88$ , then what will be the value of $\sqrt{80} + 6 \sqrt{5} = ?$

A) 13.41	B) 20.46
C) 21.66	D) 22.35

Answer & Explanation Answer: D) 22.35

Explanation:

$3 \sqrt{5} + \sqrt{125} = 17.88 \Rightarrow 3 \sqrt{5} + 5 \sqrt{5} = 17.88$

$\Rightarrow \sqrt{5} = 2.235$

$∴ \sqrt{80} + 6 \sqrt{5} = 4 \sqrt{5} + 6 \sqrt{5} = 10 \sqrt{5} = 10 \times 2.235 = 22.35$

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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 $\sqrt{18225} = 135$ , 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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