Question Detail

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}

1. \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

2. What is the square root of 0.16

0.4
0.04
0.004
4

Answer: Option A

Explanation:

as .4 * .4 = 0.16

3. Evaluate
\begin{aligned} \sqrt[3]{4\frac{12}{125}} \end{aligned}

\begin{aligned} 1\frac{2}{5} \end{aligned}
\begin{aligned} 1\frac{3}{5} \end{aligned}
\begin{aligned} 1\frac{4}{5} \end{aligned}
1

Answer: Option B

Explanation:

\begin{aligned}
= \sqrt[3]{\frac{512}{125}} \end{aligned}
\begin{aligned}
= (\frac{8*8*8}{5*5*5})^{\frac{1}{3}} \end{aligned}

\begin{aligned} = \frac{8}{5} = 1\frac{3}{5} \end{aligned}

4. The largest four digit number which is a perfect cube, is:

7000
8000
9261
9999

Answer: Option C

Explanation:

21*21*21 = 9261

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}