Question Detail

The cube root of .000216 is

0.6
0.006
0.06
.0006

Answer: Option C

1. Evaluate
\begin{aligned}
\sqrt{0.00059049}
\end{aligned}

0.00243
0.0243
0.243
2.43

Answer: Option B

Explanation:

Very obvious tip here is, after squre root the terms after decimal will be half (that is just a trick), works awesome at many questions like this.

2. The cube root of .000216 is

0.6
0.006
0.06
.0006

Answer: Option C

3. Evaluate
\begin{aligned}
\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}
\end{aligned}

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}

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. 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