Question Detail

Evaluate
\begin{aligned}
\sqrt{248+\sqrt{64}}
\end{aligned}

  • 14
  • 26
  • 16
  • 36

Answer: Option C

Explanation:

\begin{aligned}
= \sqrt{248+\sqrt{64}}
\end{aligned}

\begin{aligned}
= \sqrt{248+8}
\end{aligned}

\begin{aligned}
= \sqrt{256}
\end{aligned}

\begin{aligned}
= 16
\end{aligned}
Similar Questions :

1. \begin{aligned}
\sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9}}}}
\end{aligned}

  • 4
  • 26
  • 16
  • 6

Answer: Option D

Explanation:

\begin{aligned}
= \sqrt{41 - \sqrt{21 + \sqrt{19 - 3}}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{21 + \sqrt{16}}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{21 + 4}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{25}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{25}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - 5}
\end{aligned}

\begin{aligned}
= \sqrt{36} = 6
\end{aligned}

2. 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}

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. 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}



5. What is the square root of 0.16

  • 0.4
  • 0.04
  • 0.004
  • 4

Answer: Option A

Explanation:

as .4 * .4 = 0.16

Read more from - Square Root and Cube Root Questions Answers