Practice MCQ Questions and Answer on Square Root and Cube Root

1.

The cube root of .000216 is:

• (A) .6
• (B) .06
• (C) 77
• (D) 87

Show Answer

 $$\eqalign{ & {\left( {.000216} \right)^{\frac{1}{3}}} = {\left( {\frac{{216}}{{{{10}^6}}}} \right)^{\frac{1}{3}}} \cr & = {\left( {\frac{{6 \times 6 \times 6}}{{{{10}^2} \times {{10}^2} \times {{10}^2}}}} \right)^{\frac{1}{3}}} \cr & = \frac{6}{{{{10}^2}}} \cr & = \frac{6}{{100}} \cr & = 0.06 \cr} $$

2.

$$1728÷\sqrt[3]{262144}\times ?-288$$      = 4491

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

Show Answer

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

3.

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

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

Show Answer

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

4.

How many two-digit numbers satisfy this property. : The last digit (unit's digit) of the square of the two-digit number is 8 ?

• (A) 1
• (B) 2
• (C) 3
• (D) None of these

Show Answer

 A number ending in 8 can never be a perfect square.

5.

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

Show Answer

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

6.

The number of perfect square numbers between 50 and 1000 is = ?

• (A) 21
• (B) 22
• (C) 23
• (D) 24

Show Answer

 The first perfect square number after 50 is 64 $$\left( {64 = {8^2}} \right)$$   and the last perfect square number before 1000 is 961 $$\left[ {961 = {{\left( {31} \right)}^2}} \right]$$ So, the perfect squares between 50 and 1000 are the squares of numbers from 8 to 31. (31 - 8) + 1 = 24 Clearly, these are 24 in number.

7.

If $$\sqrt{y}=4x\text{,}$$   then $$\frac{x^2}{y}$$  is = ?

• (A) 2
• (B) $$\frac{1}{16}$$
• (C) $$\frac{1}{4}$$
• (D) 4

Show Answer

 $$\eqalign{ & \Leftrightarrow \sqrt y = 4x \cr & \Leftrightarrow y = {\left( {4x} \right)^2} \cr & \Leftrightarrow y = 16{x^2} \cr & \Leftrightarrow \frac{{{x^2}}}{y} = \frac{1}{{16}} \cr} $$

8.

$$\sqrt{\frac{0.0196}{?}}=0.2$$

• (A) 0.49
• (B) 0.7
• (C) 4.9
• (D) None of these

Show Answer

 $$\eqalign{ & {\text{Let ,}} \cr & \sqrt {\frac{{0.0196}}{x}} = 0.2 \cr & {\text{Then,}} \cr & \Leftrightarrow \frac{{0.0196}}{x} = 0.04 \cr & \Leftrightarrow x = \frac{{0.0196}}{{0.04}} \cr & \Leftrightarrow x = \frac{{1.96}}{4} \cr & \Leftrightarrow x = 0.49 \cr} $$

9.

The approximate value of $$\frac{3\sqrt{12}}{2\sqrt{28}}$$  $$÷$$ $$\frac{2\sqrt{21}}{\sqrt{98}}$$   is ?

• (A) 1.0605
• (B) 1.0727
• (C) 1.6007
• (D) 1.6026

Show Answer

 $$\eqalign{ & {\text{Given expression,}} \cr & = \frac{{3\sqrt {12} }}{{2\sqrt {28} }} \times \frac{{\sqrt {98} }}{{2\sqrt {21} }} \cr & = \frac{{3\sqrt {4 \times 3} }}{{2\sqrt {4 \times 7} }} \times \frac{{\sqrt {49 \times 2} }}{{2\sqrt {21} }} \cr & = \frac{{6\sqrt 3 }}{{4\sqrt 7 }} \times \frac{{7\sqrt 2 }}{{2\sqrt {21} }} \cr & = \frac{{21\sqrt 6 }}{{4\sqrt {7 \times 21} }} \cr & = \frac{{21\sqrt 6 }}{{28\sqrt 3 }} \cr & = \frac{3}{4}\sqrt 2 \cr & = \frac{3}{4} \times 1.414 \cr & = 3 \times 0.3535 \cr & = 1.0605 \cr} $$

10.

If $$y=5\text{,}$$   then what is the value of $$10y\sqrt{y^3-y^2}$$   = ?

• (A) $$50\sqrt{2}$$
• (B) 100
• (C) $$200\sqrt{5}$$
• (D) 500

Show Answer

 $$\eqalign{ & = 10y\sqrt {{y^3} - {y^2}} \cr & = 10 \times 5\sqrt {{5^3} - {5^2}} \cr & = 50 \times \sqrt {125 - 25} \cr & = 50 \times \sqrt {100} \cr & = 50 \times 10 \cr & = 500 \cr} $$