Practice MCQ Questions and Answer on Square Root and Cube Root

91.

$${\left[ {{{\left( {\sqrt {81} } \right)}^2}} \right]^2} = {\left( ? \right)^2}$$

• (A) 8
• (B) 9
• (C) 4096
• (D) 6561

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Answer & Solution Answer: Option E Solution: $$\eqalign{ & {\text{Let,}} \cr & {\left[ {{{\left( {\sqrt {81} } \right)}^2}} \right]^2} = {\left( x \right)^2} \cr & {\text{Then,}} \cr & \Leftrightarrow {x^2} = {\left( {81} \right)^2} \cr & \Leftrightarrow x = 81 \cr} $$

92.

One-fourth of the sum of prime numbers, greater than 4 but less than 16, is the square of = ?

• (A) 3
• (B) 4
• (C) 5
• (D) 7

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 Sum of prime numbers greater than 4 but less than 16 $$\eqalign{ & = \left( {5 + 7 + 11 + 13} \right) \cr & = 36 \cr & \therefore \frac{1}{4} \times 36 \cr & = 9 \cr & = {3^2} \cr} $$

93.

By what least number must 21600 be multiplied so as to make it perfect cube ?

• (A) 6
• (B) 10
• (C) 20
• (D) 30

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 $$21600 = {2^5} \times {3^3} \times {5^2}$$ To make it a perfect cube, it must be multiplied by (2 × 5), i.e., 10

94.

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

• (A) 57
• (B) 67
• (C) 77
• (D) 87

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 Money collected = (59.29 x 100) paise = 5929 paise. ∴ Number of members = $$\sqrt {5929} $$   = 77

95.

What is $$\frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2\sqrt {20} - \sqrt {32} + \sqrt {50} }}$$      equal to ?

• (A) 5
• (B) $$5\sqrt 2 $$
• (C) $$5\sqrt 5 $$
• (D) $$\sqrt 5 $$

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 $$\eqalign{ & {\text{Given,}} \cr & \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2\sqrt {20} - \sqrt {32} + \sqrt {50} }}{\text{ }} \cr & = \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2 \times 2\sqrt 5 - 2 \times 2\sqrt 2 + 5\sqrt 2 }} \cr & = \frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 4\sqrt 5 - 4\sqrt 2 + 5\sqrt 2 }} \cr & = \frac{{5 + \sqrt {10} }}{{\sqrt 5 + \sqrt 2 }} \cr & = \frac{{\sqrt 5 \left( {\sqrt 5 + \sqrt 2 } \right)}}{{\sqrt 5 + \sqrt 2 }} \cr & = \sqrt 5 \cr} $$

96.

$$1728 \div \root 3 \of {262144} \, \times \,?\, - 288$$      = 4491

• (A) 148
• (B) 156
• (C) 173
• (D) 177

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 $$\eqalign{ & = 262144 \cr & = 8 \times 8 \times 8 \times 8 \times 8 \times 8 \cr & = {8^6} \cr & \therefore \root 3 \of {262144} \cr & = {8^2} \cr & = 64 \cr & {\text{Let, }} \cr & {\text{1728}} \div \root 3 \of {262144} \times x - 288 = 4491 \cr & {\text{Then,}} \cr & \Leftrightarrow 1728 \div 64 \times x - 288 = 4491 \cr & \Leftrightarrow 27x = 4779 \cr & \Leftrightarrow x = \frac{{4779}}{{27}} \cr & \Leftrightarrow x = 177 \cr} $$ $$\eqalign{ & 8|262144 \cr & - - - - - - - - \cr & 8|\,\,\,32768 \cr & - - - - - - - - \cr & 8|\,\,\,\,4096 \cr & - - - - - - - - \cr & 8|\,\,\,\,\,512 \cr & - - - - - - - - \cr & 8|\,\,\,\,\,\,64 \cr & - - - - - - - - \cr & 8|\,\,\,\,\,\,\,8 \cr & - - - - - - - - \cr} $$

97.

The smallest number to be added to 680621 to make the sum a perfect square is = ?

• (A) 4
• (B) 5
• (C) 6
• (D) 8

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 $$\eqalign{ & \,\,\,\,\,\,\,\,8|\overline {68} \,\,\overline {06} \,\,\overline {21} \,(824 \cr & \,\,\,\,\,\,\,\,\,\,\,\,|\,\,64 \cr & \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,\,162|\,\,\,\,4\,06 \cr & \,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,3\,24 \cr & \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & 1644|\,\,\,\,\,\,\,\,\,\,82\,21 \cr & \,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,65\,76 \cr & \,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,16\,45 \cr & \therefore {\text{Number to be added}} \cr & = {\left( {825} \right)^2} - 680621 \cr & = 680625 - 680621 \cr & = 4 \cr} $$

98.

The value of $$\sqrt {0.121} $$   is = ?

• (A) 0.011
• (B) 0.11
• (C) 0.347
• (D) 1.1

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 $$\eqalign{ & \,\,\,\,\,3|0\,.\,\overline {12} \,\,\overline {10} \,\,\overline {00} \,\,(0.347 \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,9 \cr & \,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr & \,\,\,64|\,\,\,\,\,\,\,\,\,\,3\,10 \cr & \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,2\,56 \cr & \,\,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr & \,687|\,\,\,\,\,\,\,\,\,\,\,\,\,\,54\,00 \cr & \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,48\,00 \cr & \,\,\,\,\,\,\,\,\,\,| - - - - - - - - - - \cr & \therefore \sqrt {0.121} = 0.347 \cr} $$

99.

Given that $$\sqrt 3 = 1.732{\text{,}}$$   the value of $$\frac{{3 + \sqrt 6 }}{{5\sqrt 3 - 2\sqrt {12} - \sqrt {32} + \sqrt {50} }}$$      is ?

• (A) 1.414
• (B) 1.732
• (C) 2.551
• (D) 4.899

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 $$\eqalign{ & {\text{Given expression,}} \cr & = \frac{{3 + \sqrt 6 }}{{5\sqrt 3 - 2\sqrt {12} - \sqrt {32} + \sqrt {50} }} \cr & = \frac{{3 + \sqrt 6 }}{{5\sqrt 3 - 4\sqrt 3 - 4\sqrt 2 + 5\sqrt 2 }} \cr & = \frac{{\left( {3 + \sqrt 6 } \right)}}{{\left( {\sqrt 3 + \sqrt 2 } \right)}} \cr & = \frac{{\left( {3 + \sqrt 6 } \right)}}{{\left( {\sqrt 3 + \sqrt 2 } \right)}} \times \frac{{\left( {\sqrt 3 - \sqrt 2 } \right)}}{{\left( {\sqrt 3 - \sqrt 2 } \right)}} \cr & = \frac{{3\sqrt 3 - 3\sqrt 2 + 3\sqrt 2 - 2\sqrt 3 }}{{\left( {3 - 2} \right)}} \cr & = \sqrt 3 \cr & = 1.732 \cr} $$

100.

The value of $$\sqrt {\frac{{{{\left( {0.03} \right)}^2} + {{\left( {0.21} \right)}^2} + {{\left( {0.065} \right)}^2}}}{{{{\left( {0.003} \right)}^2} + {{\left( {0.021} \right)}^2} + {{\left( {0.0065} \right)}^2}}}} $$       is ?

• (A) 0.1
• (B) 10
• (C) $${10^2}$$
• (D) $${10^3}$$

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 $$\eqalign{ & {\text{Given expression,}} \cr & = \sqrt {\frac{{{{\left( {0.03} \right)}^2} + {{\left( {0.21} \right)}^2} + {{\left( {0.065} \right)}^2}}}{{{{\left( {\frac{{0.03}}{{10}}} \right)}^2} + {{\left( {\frac{{0.21}}{{10}}} \right)}^2} + {{\left( {\frac{{0.065}}{{10}}} \right)}^2}}}} \cr & = \sqrt {\frac{{100\left[ {{{\left( {0.03} \right)}^2} + {{\left( {0.21} \right)}^2} + {{\left( {0.065} \right)}^2}} \right]}}{{{{\left( {0.03} \right)}^2} + {{\left( {0.21} \right)}^2} + {{\left( {0.065} \right)}^2}}}} \cr & = \sqrt {100} \cr & = 10 \cr} $$