What should come in place of both the question mar | Square Roots and Cube Roots Questions & Answers

Q:

If (89)² is added to the square of a number, the answer so obtained is 16202. What is the (1/26) of that number?

A) 5.65	B) 2.7
C) 3.5	D) 6.66

Answer & Explanation Answer: C) 3.5

Explanation:

Let the number is = x

(89)² + x² = 16202

x² = 8281

x = 91

=> (1/26) of 91 = 3.5

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17 14254

Q:

What should come in place of x in the following equation?

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

A) 13	B) 12
C) 17	D) 16

Answer & Explanation Answer: B) 12

Explanation:

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

Then x² = $\sqrt{162} x \sqrt{128}$

= Sqrt of 8² x 6² x 3²

= 8 x 6 x 3

x² = 144.

x = 12.

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8 6904

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:

If $x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}}$ then find the value of $x^{3} - 6 x^{2} + 6 x$ ?

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

Answer & Explanation Answer: B) 2

Explanation:

Given that $x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}}$

So x - 2 = $2^{\frac{2}{3}} + 2^{\frac{1}{3}}$

Now cubing on both sides, we get

=> $x^{3} - 8 - 6 x^{2} + 12 x = 4 + 2 + 6 (x - 2)$

Therefore, $x^{3} - 6 x^{2} + 6 x = - 6 + 8 = 2$

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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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7 3102

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:

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

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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13 3642

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

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

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

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What should come in place of both the question marks in the equation ?128=162?

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

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