Square Root And Cube Root - Aptitude MCQ Questions and Solutions with Explanations Page-10 section-1

91.
Given $$\sqrt 5 = 2.2361,$$ $$\sqrt 3 = 1.7321{\text{,}}$$ then $$\frac{1}{{\sqrt 5 - \sqrt 3 }}$$ is equal to ?

A. 1.98

B. 1.984

C. 1.9841

D. 2

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92.
$$\frac{1}{{\left( {\sqrt 9 - \sqrt 8 } \right)}} \, - $$ $$\frac{1}{{\left( {\sqrt 8 - \sqrt 7 } \right)}} \, + $$ $$\frac{1}{{\left( {\sqrt 7 - \sqrt 6 } \right)}} \, - $$ $$\frac{1}{{\left( {\sqrt 6 - \sqrt 5 } \right)}} \, + $$ $$\frac{1}{{\left( {\sqrt 5 - \sqrt 4 } \right)}}$$ is equal to ?

A. 0

B. $$\frac{1}{3}$$

C. 1

D. 5

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93.
Determined the value of $$\frac{1}{{\sqrt 1 + \sqrt 2 }}{\text{ + }}$$ $$\frac{1}{{\sqrt 2 + \sqrt 3 }}\, + $$ $$\frac{1}{{\sqrt 3 + \sqrt 4 }}\, + $$ $$...... + $$ $$\frac{1}{{\sqrt {120} + \sqrt {121} }}{\text{ = ?}}$$

A. 8

B. 10

C. $$\sqrt {120} $$

D. $$12\sqrt 2 $$

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94.
If $$\sqrt 2 = 1.414{\text{,}}$$ the square root of $$\frac{{\sqrt 2 - 1}}{{\sqrt 2 + 1}}$$ is nearest to = ?

A. 0.172

B. 0.414

C. 0.586

D. 1.414

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95.
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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96.
$$\left( {\frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }} + \frac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }} + \frac{{\sqrt 3 - 1}}{{\sqrt 3 + 1}}} \right)$$ simplifies to = ?

A. $$16 - \sqrt 3 $$

B. $$4 - \sqrt 3 $$

C. $$2 - \sqrt 3 $$

D. $$2 + \sqrt 3 $$

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97.
If $$x = 3 + \sqrt 8 ,$$ then $${x^2} + \frac{1}{{{x^2}}}$$ is equal to = ?

A. 30

B. 34

C. 36

D. 38

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98.
If $$a = \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }},$$ $$b = \frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 + \sqrt 2 }}$$ then the value of $${a^2} + {b^2}$$ would be = ?

A. 10

B. 98

C. 99

D. 100

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99.
If $$a = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}}$$ and $$b = \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}}, $$ the value of $$\left( {\frac{{{a^2} + ab + {b^2}}}{{{a^2} - ab + {b^2}}}} \right)$$ is ?

A. $$\frac{3}{4}$$

B. $$\frac{4}{3}$$

C. $$\frac{3}{5}$$

D. $$\frac{5}{3}$$

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Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{ }}a = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}} \cr & \,\,\,\,\,\, {\text{ = }}\frac{{\left( {\sqrt 5 + 1} \right)}}{{\left( {\sqrt 5 - 1} \right)}} \times \frac{{\left( {\sqrt 5 + 1} \right)}}{{\left( {\sqrt 5 + 1} \right)}} \cr & \,\,\,\,\,\,\, = \frac{{{{\left( {\sqrt 5 + 1} \right)}^2}}}{{\left( {5 - 1} \right)}} \cr & \,\,\,\,\,\,\, = \frac{{5 + 1 + 2\sqrt 5 }}{4} \cr & \,\,\,\,\,\,\, = \left( {\frac{{3 + \sqrt 5 }}{2}} \right) \cr & {\text{ }}b = \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}} \cr & \,\,\,\,\,\,\, = \frac{{\left( {\sqrt 5 - 1} \right)}}{{\left( {\sqrt 5 + 1} \right)}} \times \frac{{\left( {\sqrt 5 - 1} \right)}}{{\left( {\sqrt 5 - 1} \right)}} \cr & \,\,\,\,\,\,\, = \frac{{{{\left( {\sqrt 5 - 1} \right)}^2}}}{{\left( {5 - 1} \right)}} \cr & \,\,\,\,\,\,\, = \frac{{5 + 1 - 2\sqrt 5 }}{4} \cr & \,\,\,\,\,\,\, = \left( {\frac{{3 - \sqrt 5 }}{2}} \right) \cr & \,\,\,\,\,\,\, \therefore {a^2} + {b^2} \cr & \,\,\,\,\,\,\, = {\left( {\frac{{3 + \sqrt 5 }}{2}} \right)^2} + {\left( {\frac{{3 - \sqrt 5 }}{2}} \right)^2} \cr & \,\,\,\,\,\,\, = \frac{{{{\left( {3 + \sqrt 5 } \right)}^2}}}{4} + \frac{{{{\left( {3 - \sqrt 5 } \right)}^2}}}{4} \cr & \,\,\,\,\,\,\, = \frac{{{{\left( {3 + \sqrt 5 } \right)}^2} + {{\left( {3 - \sqrt 5 } \right)}^2}}}{4} \cr & \,\,\,\,\,\,\, = \frac{{9 + 2.3.\sqrt 5 + 5 + 9 - 2.3.\sqrt 5 + 5}}{4} \cr & \,\,\,\,\,\,\, = \frac{{2\left( {9 + 5} \right)}}{4} \cr & \,\,\,\,\,\,\, = \frac{{28}}{4} \cr & \,\,\,\,\,\,\, = 7 \cr & {\text{Also, }} \cr & ab = \frac{{\left( {3 + \sqrt 5 } \right)}}{2} \times \frac{{\left( {3 - \sqrt 5 } \right)}}{2} \cr & \,\,\,\,\,\,\, = \frac{{\left( {9 - 5} \right)}}{4} \cr & \,\,\,\,\,\,\, = 1 \cr & \,\,\,\,\,\,\, \therefore \left( {\frac{{{a^2} + ab + {b^2}}}{{{a^2} - ab + {b^2}}}} \right) \cr & \,\,\,\,\,\,\, = \frac{{\left( {{a^2} + {b^2}} \right) + ab}}{{\left( {{a^2} + {b^2}} \right) - ab}} \cr & \,\,\,\,\,\,\, = \frac{{7 + 1}}{{7 - 1}} \cr & \,\,\,\,\,\,\, = \frac{8}{6} \cr & \,\,\,\,\,\,\, = \frac{4}{3} \cr} $$

100.
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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Square Root And Cube Root - Aptitude MCQ Questions and Solutions with Explanations

91. Given $$\sqrt 5 = 2.2361,$$ $$\sqrt 3 = 1.7321{\text{,}}$$ then $$\frac{1}{{\sqrt 5 - \sqrt 3 }}$$ is equal to ?

Answer & Solution

Answer & Solution

93. Determined the value of $$\frac{1}{{\sqrt 1 + \sqrt 2 }}{\text{ + }}$$ $$\frac{1}{{\sqrt 2 + \sqrt 3 }}\, + $$ $$\frac{1}{{\sqrt 3 + \sqrt 4 }}\, + $$ $$...... + $$ $$\frac{1}{{\sqrt {120} + \sqrt {121} }}{\text{ = ?}}$$

Answer & Solution

94. If $$\sqrt 2 = 1.414{\text{,}}$$ the square root of $$\frac{{\sqrt 2 - 1}}{{\sqrt 2 + 1}}$$ is nearest to = ?

Answer & Solution

95. 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 ?

Answer & Solution

96. $$\left( {\frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }} + \frac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }} + \frac{{\sqrt 3 - 1}}{{\sqrt 3 + 1}}} \right)$$ simplifies to = ?

Answer & Solution

97. If $$x = 3 + \sqrt 8 ,$$ then $${x^2} + \frac{1}{{{x^2}}}$$ is equal to = ?

Answer & Solution

98. If $$a = \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }},$$ $$b = \frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 + \sqrt 2 }}$$ then the value of $${a^2} + {b^2}$$ would be = ?

Answer & Solution

99. If $$a = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}}$$ and $$b = \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}}, $$ the value of $$\left( {\frac{{{a^2} + ab + {b^2}}}{{{a^2} - ab + {b^2}}}} \right)$$ is ?

Answer & Solution

100. 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 ?

Answer & Solution

Read More Section(Square Root and Cube Root)

91.
Given $$\sqrt 5 = 2.2361,$$ $$\sqrt 3 = 1.7321{\text{,}}$$ then $$\frac{1}{{\sqrt 5 - \sqrt 3 }}$$ is equal to ?

93.
Determined the value of $$\frac{1}{{\sqrt 1 + \sqrt 2 }}{\text{ + }}$$ $$\frac{1}{{\sqrt 2 + \sqrt 3 }}\, + $$ $$\frac{1}{{\sqrt 3 + \sqrt 4 }}\, + $$ $$...... + $$ $$\frac{1}{{\sqrt {120} + \sqrt {121} }}{\text{ = ?}}$$

94.
If $$\sqrt 2 = 1.414{\text{,}}$$ the square root of $$\frac{{\sqrt 2 - 1}}{{\sqrt 2 + 1}}$$ is nearest to = ?

95.
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 ?

96.
$$\left( {\frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }} + \frac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }} + \frac{{\sqrt 3 - 1}}{{\sqrt 3 + 1}}} \right)$$ simplifies to = ?

97.
If $$x = 3 + \sqrt 8 ,$$ then $${x^2} + \frac{1}{{{x^2}}}$$ is equal to = ?

98.
If $$a = \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }},$$ $$b = \frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 + \sqrt 2 }}$$ then the value of $${a^2} + {b^2}$$ would be = ?

99.
If $$a = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}}$$ and $$b = \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}}, $$ the value of $$\left( {\frac{{{a^2} + ab + {b^2}}}{{{a^2} - ab + {b^2}}}} \right)$$ is ?

100.
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 ?