Question Detail

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

1. Evaluate $\begin{aligned} \sqrt{1471369} \end{aligned}$

1213
1223
1233
1243

Answer: Option A

2. The cube root of .000216 is

0.6
0.006
0.06
.0006

Answer: Option C

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

Answer: Option D

Explanation:

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

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

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

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

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

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

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

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

Answer: Option C

Explanation:

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

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

5. 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:

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

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