Practice MCQ Questions and Answer on Square Root and Cube Root

81.

Given $$\sqrt 2 = 1.414.$$   Then the value of $$\sqrt 8 $$  $$ + $$ $$2\sqrt {32} $$  $$ - $$ $$3\sqrt {128} $$  $$ + $$ $$4\sqrt {50} $$   is = ?

• (A) 8.426
• (B) 8.484
• (C) 8.526
• (D) 8.876

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 Given expression, $$\sqrt {4 \times 2} + 2\sqrt {16 \times 2} - 3\sqrt {64 \times 2} $$       $$ + $$ $$4\sqrt {25 \times 2} $$ $$\eqalign{ & = 2\sqrt 2 + 8\sqrt 2 - 24\sqrt 2 + 20\sqrt 2 \cr & = 6\sqrt 2 \cr & = 6 \times 1.414 \cr & = 8.484 \cr} $$

82.

If $$0.13 \div {p^2} = 13{\text{,}}$$   then p equals = ?

• (A) 0.01
• (B) 0.1
• (C) 10
• (D) 100

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 $$\eqalign{ & \Leftrightarrow \frac{{0.13}}{{{p^2}}} = 13 \cr & \Leftrightarrow {p^2} = \frac{{0.13}}{{13}} \cr & \Leftrightarrow {p^2} = \frac{1}{{100}} \cr & \Leftrightarrow p = \sqrt {\frac{1}{{100}}} \cr & \Leftrightarrow p = \frac{1}{{10}} \cr & \Leftrightarrow p = 0.1 \cr} $$

83.

The least number of 4 digits which is a perfect square is = ?

• (A) 1000
• (B) 1016
• (C) 1024
• (D) 1036

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 Least number of 4 digits is 1000 $$\eqalign{ & \,\,\,\,3|\overline {10} \,\,\overline {00} \,\,(31 \cr & \,\,\,\,\,\,\,|\,\,\,\,9 \cr & \,\,\,\,\,\,\,| - - - - - - \cr & 61|\,\,\,\,\,1\,00 \cr & \,\,\,\,\,\,\,|\,\,\,\,\,\,61 \cr & \,\,\,\,\,\,\,| - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,39 \cr & \therefore {\left( {31} \right)^2} 1000 {\left( {32} \right)^2} \cr & {\text{Hence, required number}} \cr & = {\left( {32} \right)^2} \cr & = 1024 \cr} $$

84.

What is the least number which should be subtracted 0.000326 in order to make it a perfect square = ?

• (A) 0.000002
• (B) 0.000004
• (C) 0.02
• (D) 0.04

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 $$\eqalign{ & 0.000326 = \frac{{326}}{{{{10}^6}}} \cr & \,\,\,\,1|\overline 3 \,\,\overline {26} \,\,(18 \cr & \,\,\,\,\,\,\,|\,\,1 \cr & \,\,\,\,\,\,\,| - - - - - - \cr & 28|\,\,\,2\,26 \cr & \,\,\,\,\,\,\,|\,\,\,2\,24 \cr & \,\,\,\,\,\,\,| - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2 \cr} $$ ∴ Required number to be subtracted $$\eqalign{ & = \frac{2}{{{{10}^6}}} \cr & = 0.000002 \cr} $$

85.

$$\sqrt {110.25} \times \sqrt {0.01} \, \div $$    $$\sqrt {0.0025} $$   $$ - $$ $$\sqrt {420.25} $$  equals ?

• (A) 0.50
• (B) 0.64
• (C) 0.73
• (D) 0.75

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 Given expression, $$ = \sqrt {\frac{{11025}}{{100}}} \times \sqrt {\frac{1}{{100}}} \, \div \,$$    $$\sqrt {\frac{{25}}{{10000}}} \, - \,$$ $$\,\sqrt {\frac{{42025}}{{100}}} $$ $$\eqalign{ & = \frac{{105}}{{10}} \times \frac{1}{{10}} \div \frac{5}{{100}} - \frac{{205}}{{10}} \cr & = \frac{{105}}{{100}} \times \frac{{100}}{5} - \frac{{205}}{{10}} \cr & = 21 - \frac{{205}}{{10}} \cr & = \frac{{210 - 205}}{{10}} \cr & = \frac{5}{{10}} \cr & = \frac{1}{2} \cr & = 0.50 \cr} $$

86.

If $$a = 0.1039{\text{,}}$$   then the value of $$\sqrt {4{a^2} - 4a + 1} $$    $$ + $$ $$3a$$  is ?

• (A) 0.1039
• (B) 0.2078
• (C) 1.1039
• (D) 2.1039

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 $$\eqalign{ & = \sqrt {4{a^2} - 4a + 1} + 3a \cr & = \sqrt {{{\left( 1 \right)}^2} + {{\left( {2a} \right)}^2} - 2 \times 1 \times 2a} + 3a \cr & = \sqrt {{{\left( {1 - 2a} \right)}^2}} + 3a \cr & = \left( {1 - 2a} \right) + 3a \cr & = \left( {1 + a} \right) \cr & = \left( {1 + 0.1039} \right) \cr & = 1.1039 \cr} $$

87.

One-fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels ?

• (A) 32
• (B) 34
• (C) 35
• (D) 36

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 Let the total number of camels be x Then, $$\eqalign{ & \Leftrightarrow x - \left( {\frac{x}{4} + 2\sqrt x } \right) = 15 \cr & \Leftrightarrow \frac{{3x}}{4} - 2\sqrt x = 15 \cr & \Leftrightarrow 3x - 8\sqrt x = 60 \cr & \Leftrightarrow 8\sqrt x = 3x - 60 \cr & \Leftrightarrow 64x = {\left( {3x - 60} \right)^2} \cr & \Leftrightarrow 64x = 9{x^2} + 3600 - 360x \cr & \Leftrightarrow 9{x^2} - 424x + 3600 = 0 \cr & \Leftrightarrow 9{x^2} - 324x - 100x + 3600 = 0 \cr & \Leftrightarrow 9x\left( {x - 36} \right) - 100\left( {x - 36} \right) = 0 \cr & \Leftrightarrow \left( {x - 36} \right)\left( {9x - 100} \right) = 0 \cr & \Leftrightarrow x = 36\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\because x \ne \frac{{100}}{9}} \right] \cr} $$

88.

If $$\sqrt {1369} + \sqrt {0.0615 + x} $$      = 37.25, the x is equal to ?

• (A) $${10^{ - 1}}$$
• (B) $${10^{ - 2}}$$
• (C) $${10^{ - 3}}$$
• (D) None of these

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 $$\eqalign{ & \Leftrightarrow 37 + \sqrt {0.0615 + x} = 37.25 \cr & \Leftrightarrow \sqrt {0.0615 + x} = 0.25 \cr & \Leftrightarrow 0.0615 + x = {\left( {0.25} \right)^2} = 0.0625 \cr & \Leftrightarrow x = 0.001 \cr & \Leftrightarrow x = \frac{1}{{{{10}^3}}} \cr & \Leftrightarrow x = {10^{ - 3}} \cr} $$

89.

The square root of 41209 is equal to = ?

• (A) 103
• (B) 203
• (C) 303
• (D) 403

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 $$\eqalign{ & \,\,\,\,\,2|4\,\,\overline {12} \,\,\overline {09} \,(203 \cr & \,\,\,\,\,\,\,\,\,|4 \cr & \,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,40|\,\,\,\,\,\,\,\,12 \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,0 \cr & \,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,12\,09 \cr & 403|\,\,\,\,\,\,\,\,\,12\,09 \cr & \,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,x \cr & \,\,\,\,\,\,\,\,\,| - - - - - - - - \, \cr & \therefore \sqrt {41209} = 203 \cr} $$

90.

$$\root 3 \of {\sqrt {0.000064} } = ?$$

• (A) 0.02
• (B) 0.2
• (C) 2
• (D) None of these

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 $$\eqalign{ & = \sqrt {0.000064} \cr & = \sqrt {\frac{{64}}{{{{10}^6}}}} \cr & = \frac{8}{{{{10}^3}}} \cr & = \frac{8}{{1000}} \cr & = 0.008 \cr & \therefore \root 3 \of {\sqrt {0.000064} } \cr & = \root 3 \of {0.008} \cr & = \root 3 \of {\frac{8}{{1000}}} \cr & = \frac{2}{{10}} \cr & = 0.2 \cr} $$