Question Detail
The cube root of .000216 is
- 0.6
- 0.006
- 0.06
- .0006
Answer: Option C
1. Evaluate
\begin{aligned}
\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}
\end{aligned}
- 16
- 8
- 6
- 4
Answer: Option D
Explanation:
\begin{aligned}
= \sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}
\end{aligned}
\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}
\end{aligned}
\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}
\end{aligned}
\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}}
\end{aligned}
\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{108+13}}}
\end{aligned}
\begin{aligned}
=\sqrt{10+\sqrt{25+\sqrt{121}}}
\end{aligned}
\begin{aligned}
=\sqrt{10+\sqrt{25+11}}
\end{aligned}
\begin{aligned}
=\sqrt{10+\sqrt{36}}
\end{aligned}
\begin{aligned}
=\sqrt{10+6}
\end{aligned}
\begin{aligned}
=\sqrt{16} = 4
\end{aligned}
2. The least perfect square, which is divisible by each of 21, 36 and 66 is
- 213414
- 213424
- 213434
- 213444
Answer: Option D
Explanation:
L.C.M. of 21, 36, 66 = 2772
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444
3. \begin{aligned}
(\frac{\sqrt{625}}{11} \times \frac{14}{\sqrt{25}} \times \frac{11}{\sqrt{196}})
\end{aligned}
- 15
- 7
- 5
- 9
Answer: Option C
Explanation:
\begin{aligned}
= (\frac{25}{11} \times \frac{14}{5} \times \frac{11}{14})
\end{aligned}
\begin{aligned}
= 5
\end{aligned}
4. Evaluate
\begin{aligned}
\sqrt{1\frac{9}{16}}
\end{aligned}
- \begin{aligned} 1\frac{1}{6} \end{aligned}
- \begin{aligned} 1\frac{1}{5} \end{aligned}
- \begin{aligned} 1\frac{1}{4} \end{aligned}
- \begin{aligned} 1\frac{1}{3} \end{aligned}
Answer: Option C
Explanation:
\begin{aligned}
= \sqrt{\frac{25}{16}}
\end{aligned}
\begin{aligned}
= \frac{\sqrt{25}}{\sqrt{16}}
\end{aligned}
\begin{aligned}
= \frac{5}{4}
\end{aligned}
\begin{aligned}
= 1\frac{1}{4}
\end{aligned}
5. if a = 0.1039, then the value of
\begin{aligned} \sqrt{4a^2 - 4a + 1} + 3a \end{aligned}
- 12.039
- 1.2039
- 11.039
- 1.1039
Answer: Option D
Explanation:
Tip: Please check the question carefully before answering. As 3a is not under the root we can convert it into a formula , lets evaluate now :
\begin{aligned}
= \sqrt{4a^2 - 4a + 1} + 3a \end{aligned}
\begin{aligned}
= \sqrt{(1)^2 + (2a)^2 - 2x1x2a} + 3a \end{aligned}
\begin{aligned}
= \sqrt{(1-2a)^2} + 3a \end{aligned}
\begin{aligned}
= (1-2a) + 3a \end{aligned}
\begin{aligned}
= (1-2a) + 3a \end{aligned}
\begin{aligned}
= 1 + a = 1 + 0.1039 = 1.1039 \end{aligned}