This set of Aptitude Questions and Answers (MCQs) focuses on “Square Root – Set 2”.
1. If \(\sqrt{961}\)=31, then find the value of \(\sqrt{9.61}-\sqrt{0.0961}-\sqrt{0.000961}+\sqrt{96100}\).
a) 312.759
b) 302.719
c) 322.689
d) 324.811
View Answer
Explanation: \(\sqrt{9.61}-\sqrt{0.0961}-\sqrt{0.000961}+\sqrt{96100}\)=3.1-0.31-0.031+310=312.759.
2. Find the value of √5 up-to three decimal places.
a) 2.225
b) 2.236
c) 2.238
d) 2.228
View Answer
Explanation: √5=2.236.
3. What is the value of \(\frac{1}{\sqrt{900} – \sqrt{899}} – \frac{1}{\sqrt{899}-\sqrt{898}} + \frac{1}{\sqrt{898}-\sqrt{897}} – \frac{1}{\sqrt{897}-\sqrt{896}}+⋯+\frac{1}{\sqrt{2}-\sqrt{1}}\).
a) 30
b) 31
c) 29
d) 0
View Answer
Explanation: = \(\frac{1}{\sqrt{900} – \sqrt{899}} – \frac{1}{\sqrt{899}-\sqrt{898}} + \frac{1}{\sqrt{898}-\sqrt{897}} – \frac{1}{\sqrt{897}-\sqrt{896}}+⋯+\frac{1}{\sqrt{2}-\sqrt{1}}\)
= \(\frac{1}{\sqrt{900}-\sqrt{899}}*\frac{\sqrt{900}+\sqrt{899}}{\sqrt{900}+\sqrt{899}}-\frac{1}{\sqrt{899}-\sqrt{898}}*\frac{\sqrt{899}+\sqrt{898}}{\sqrt{899}+\sqrt{898}}+\frac{1}{\sqrt{898}-\sqrt{897}}*\frac{\sqrt{898}+\sqrt{897}}{\sqrt{898}+\sqrt{897}}-\frac{1}{\sqrt{897}-√896}*\frac{\sqrt{897}+\sqrt{896}}{\sqrt{897}+\sqrt{896}} \) \( +⋯+\frac{1}{\sqrt{2}-\sqrt{1}}*\frac{\sqrt{2}+\sqrt{1}}{\sqrt{2}+\sqrt{1}} \)
= \(\frac{\sqrt{900}+\sqrt{899}}{900-899}-\frac{\sqrt{899}+\sqrt{898}}{899-898}+\frac{\sqrt{898}+\sqrt{897}}{898-897}-\frac{\sqrt{897}+\sqrt{896}}{897-896}+⋯-\frac{\sqrt{3}+\sqrt{2}}{3-2}+\frac{\sqrt{2}+\sqrt{1}}{2-1}\).
= \(\sqrt{900}+\sqrt{899}-\sqrt{899}-\sqrt{898}+\sqrt{898}+\sqrt{897}-\sqrt{897}-\sqrt{896}+⋯-\sqrt{3}-\sqrt{2}+\sqrt{2}+\sqrt{1}\).
= \(\sqrt{900}+\sqrt{1}\)=30+1=31.
4. Find the sum of 9+\(\frac{1}{√9}+\frac{1}{9+√9}-\frac{1}{9-√9}\).
a) 11.45
b) 10.5
c) 8.75
d) 9.25
View Answer
Explanation: 9+\(\frac{1}{√9}+\frac{1}{9+√9}-\frac{1}{9-√9}\)=9+\(\frac{1}{3}+\frac{1}{9+3}-\frac{1}{9-3}\)=9+\(\frac{1}{3}+\frac{1}{12}+\frac{1}{6}=\frac{37}{4}\)=9.25.
5. If √6=2.449, then find the value of \(\sqrt{216}-\frac{1}{3}\sqrt{486}-\sqrt{24}\).
a) 2.449
b) 4.898
c) 7.347
d) 1.2245
View Answer
Explanation: \(\sqrt{216}-\frac{1}{3}\sqrt{486}-\sqrt{24}=\sqrt{36*6}-\frac{1}{3} \sqrt{81*6}-\sqrt{4*6}=6\sqrt{6}-\frac{1}{3}*9\sqrt{6}+2\sqrt{6}\).
=6√6-3√6+2√6=√6=2.449.
6. Find the value of \(\sqrt{0.144}\) up to four decimal places.
a) 1.2
b) 0.12
c) 0.3794
d) 0.3829
View Answer
Explanation: \(\sqrt{0.144}\)=0.3794.
7. If \(\sqrt{0.09*0.9*p}\)=0.9*0.09*√q, then find the value of p/q.
a) 0.81
b) 1
c) 0.081
d) 10
View Answer
Explanation: \(\sqrt{0.09*0.9*p}\) = 0.9*0.09*√q 🡪 \(\frac{√p}{√q}=\frac{0.9*0.09}{√0.09*√0.9} 🡪 \frac{p}{q}=\frac{0.9*0.09*0.9*0.09}{0.9*0.09}\) = 0.081.
8. Find the square root of 0.159.
a) 4/15
b) 13/30
c) 11/30
d) 2/5
View Answer
Explanation: 0.159=\(\frac{159-15}{900}=\frac{144}{900}\).
\(\sqrt{0.15\overline{9}}=\sqrt{\frac{144}{900}}=\frac{12}{30}=\frac{2}{5}\).
9. Find the greatest 8-digit number which is a perfect square.
a) 998001
b) 999000
c) 999001
d) 998011
View Answer
Explanation: Greatest 8-digit number = 99999999.
Greatest 8-digit perfect square number = 99999999 – 19998 = 99980001.
10. Find the least square number which is divisible by 24, 25, 30 and 36
a) 900
b) 1600
c) 3600
d) 2500
View Answer
Explanation: LCM of 12, 15, 25 and 36 is 1800.
1800 = 22*2*32*52.
To make it perfect square, it should be multiplied by 2. 🡪 1800*2 = 3600.
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