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What is the smallest number by which 3600 be divided to make it a perfect cube.

  • 450
  • 445
  • 440
  • 430

Answer: Option A

Explanation:

\begin{aligned}
3600 = 2^3 \times 5^2 \times 3^2 \times 2
\end{aligned}
To make it a perfect cube it must be divided by
\begin{aligned}
5^2 \times 3^2 \times 2 = 450
\end{aligned}

Similar Questions :

1. The cube root of .000216 is

  • 0.6
  • 0.006
  • 0.06
  • .0006

Answer: Option C

2. \begin{aligned} \sqrt{\frac{0.081 * 0.484 }{0.0064 * 6.25}} \end{aligned}

  • 0.66
  • 0.77
  • 0.88
  • 0.99

Answer: Option D

3. \begin{aligned} \sqrt{0.00059049} \end{aligned}

  • 24.3
  • 2.43
  • 0.243
  • 0.0243

Answer: Option D

4. 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

5. 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}

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