Question Detail

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.

1. 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}

2. Evaluate \begin{aligned} \sqrt[3]{\sqrt{.000064}} \end{aligned}

0.0002
0.002
0.02
0.2

Answer: Option D

Explanation:

\begin{aligned} = \sqrt{.000064} \end{aligned}
\begin{aligned} = \sqrt{\frac{64}{10^6}} \end{aligned}
\begin{aligned} = \frac{8}{10^3} = .008 \end{aligned}
\begin{aligned} = \sqrt[3]{.008} \end{aligned}
\begin{aligned} = \sqrt[3]{\frac{8}{1000}} \end{aligned}
\begin{aligned} = \frac{2}{10} = 0.2 \end{aligned}

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{53824}
\end{aligned}

Answer: Option B

5. 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}

Question Detail

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

1. if a = 0.1039, then the value of \begin{aligned} \sqrt{4a^2 - 4a + 1} + 3a \end{aligned}

2. Evaluate \begin{aligned} \sqrt[3]{\sqrt{.000064}} \end{aligned}

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

4. Evaluate \begin{aligned} \sqrt{53824} \end{aligned}

5. Evaluate \begin{aligned} \sqrt{1\frac{9}{16}} \end{aligned}

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

1. if a = 0.1039, then the value of
\begin{aligned} \sqrt{4a^2 - 4a + 1} + 3a \end{aligned}

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

4. Evaluate
\begin{aligned}
\sqrt{53824}
\end{aligned}

5. Evaluate
\begin{aligned}
\sqrt{1\frac{9}{16}}
\end{aligned}