What should come in place of x in the followi | Square Roots and Cube Roots Questions & 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

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

12 3961

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:

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

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

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

6 3428

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:

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

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

7 3349

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:

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

$\Rightarrow \sqrt{5} = 2.235$

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

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

14 7055

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:

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

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

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

10 3257

Q:

$28 \sqrt{?} + 1426 = \frac{3}{4} o f 2872$

A) 576	B) 676
C) 1296	D) 1444

Answer & Explanation Answer: B) 676

Explanation:

$L e t 28 \sqrt{x} + 1426 = 3 \times 718$

Then $28 \sqrt{x} = 2154 - 1426$

$\Rightarrow 28 \sqrt{x} = 728 \Rightarrow \sqrt{x} = 26$

$∴ x = 676$

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

9 3638

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

$∴ x = 12$

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

21 10066

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

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

25 6021

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

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

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

Quick Links

What should come in place of x in the following equation? x128 = 162x

Quick Links

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

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