Question Detail

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}

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. \begin{aligned}
(\frac{\sqrt{625}}{11} \times \frac{14}{\sqrt{25}} \times \frac{11}{\sqrt{196}})
\end{aligned}

Answer: Option C

Explanation:

\begin{aligned}
= (\frac{25}{11} \times \frac{14}{5} \times \frac{11}{14})
\end{aligned}

\begin{aligned}
= 5
\end{aligned}

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

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}

4. 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}

5. 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}