Practice MCQ Questions and Answer on Square Root and Cube Root

21.

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

• (A) 8
• (B) 9
• (C) 4096
• (D) 6561

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

22.

The square root of 123454321 is = ?

• (A) 111111
• (B) 12341
• (C) 11111
• (D) 11211

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 $$\therefore \sqrt {123454321} = 11111$$

23.

If $$\sqrt 5 = 2.236{\text{,}}$$   then the value of $$\frac{1}{{\sqrt 5 }}$$  is = ?

• (A) 0.367
• (B) 0.447
• (C) 0.745
• (D) None of these

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 $$\eqalign{ & = \frac{1}{{\sqrt 5 }} \cr & = \frac{1}{{\sqrt 5 }} \times \frac{{\sqrt 5 }}{{\sqrt 5 }} \cr & = \frac{{\sqrt 5 }}{5} \cr & = \frac{{2.236}}{5} \cr & = 0.447 \cr} $$

24.

The square root of $$\frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}}$$ $${\text{ + }}$$$$\left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right]$$    is = ?

• (A) 1
• (B) 2
• (C) 3
• (D) 4

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 $$\frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}}$$ $${\text{ + }}$$$$\left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right]$$ $$ = \frac{{{{\left( {0.75} \right)}^2} \times 0.75}}{{0.25}}$$   $${\text{ + }}$$ $$\left[ {0.75 + 0.5625 + 1} \right]$$ $$ = 0.5625 \times 3 \,\, + $$   $$\left[ {0.75 + 0.5625 + 1} \right]$$ $$\eqalign{ & = 1.6875 + 2.3125 \cr & = 4 \cr} $$ Square root of 4 = 2

25.

If $$\sqrt {33} = 5.745{\text{,}}$$   then which of the following values is approximately $$\sqrt {\frac{3}{{11}}} {\text{ ?}}$$

• (A) 1
• (B) 6.32
• (C) 0.5223
• (D) 2.035

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 $$\eqalign{ & = \sqrt {\frac{3}{{11}}} \cr & = \sqrt {\frac{{3 \times 11}}{{11 \times 11}}} \cr & = \frac{{\sqrt {33} }}{{11}} \cr & = \frac{{5.745}}{{11}} \cr & = 0.5223 \cr} $$

26.

The square root of 535.9225 is = ?

• (A) 23.15
• (B) 23.45
• (C) 24.15
• (D) 28.25

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 $$\eqalign{ & = \sqrt {{\text{535}}{\text{.9225}}} \cr & = \sqrt {\frac{{{\text{5359225}}}}{{10000}}} \cr & = \frac{{2315}}{{100}} \cr & = 23.15 \cr & \,\,\,\,\,\,\,\,\,2|\overline 5 \,\,\overline {35} \,\,\overline {92} \,\,\overline {25} \,\,(2315 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|4 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,\,\,\,\,\,43|\,\,1\,35 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,1\,2\,9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,\,461\,|\,\,\,\,\,\,\,\,\,6\,92 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,4\,61 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr & 4625\,|\,\,\,\,\,\,\,\,\,\,\,\,231\,25 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,231\,25 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{x}} \cr} $$

27.

The square root of 41209 is equal to = ?

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

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

28.

$$\sqrt {\sqrt {17956} + \sqrt {24025} } = ?$$

• (A) 19
• (B) 155
• (C) 256
• (D) 289

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Answer & Solution Answer: Option E Solution: $$\eqalign{ & \sqrt {\sqrt {17956} + \sqrt {24025} } \cr & = \sqrt {134 + 155} \cr & = \sqrt {289} \cr & = 17 \cr} $$

29.

Which of the following is closest to $$\sqrt 3 = \,?$$

• (A) 1.69
• (B) $$\frac{{173}}{{100}}$$
• (C) 1.75
• (D) $$\frac{9}{5}$$

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 $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,1|\overline 3 \,.\,\,\overline {00} \,\,\overline {00} \,\,\overline {00} \,(1.732 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|1 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,\,\,\,\,27|\,\,2\,\,\,00 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,1\,\,\,89 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr & \,\,\,343\,|\,\,\,\,\,\,\,\,\,11\,\,00 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,10\,\,29 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr & 3492\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,71\,\,00 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,69\,\,84 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,16 \cr} $$ $$\eqalign{ & \therefore \sqrt 3 \cr & = 1.73 \cr & = \frac{{173}}{{100}} \cr} $$

30.

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