(7 + 35)(7 - 35) = (7)² - (35)²  = 49 - 45  = 4  = 2.

Answer : Option C

Explanation :

$MF#%\sqrt{0.000256 \times x} = 1.6 \\\\ \Rightarrow 0.000256 \times x = (1.6)^2 \\\\ \Rightarrow 0.000256\times x = 2.56 \\\\ \Rightarrow x = \dfrac{2.56}{0.000256} = \dfrac{2560000}{256} = 10000$MF#%

√0.0009
= √(9 / 10000)
= 3 / 100
= 0.03.

√(1 + (x / 144)) = 13 / 12
( 1 + (x / 144)) = (13 / 12 )²
= 169 / 144
x / 144 = (169 / 144) - 1
x / 144 = 25/144
x = 25.

Answer : Option B

Explanation :

$MF#%\begin{align}&x = \dfrac{\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)} = \dfrac{\left(\sqrt{3}+1\right)\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)} = \dfrac{\left(\sqrt{3}+1\right)^2}{3-1} = \dfrac{3 + 2\sqrt{3} + 1}{2}= \dfrac{4 + 2\sqrt{3}}{2} = 2 + \sqrt{3}\\\\
&y = \dfrac{\sqrt{3}-1}{\sqrt{3}+1}= \dfrac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)} = \dfrac{\left(\sqrt{3}-1\right)^2}{3-1} = \dfrac{3 - 2\sqrt{3} + 1}{2}= \dfrac{4 - 2\sqrt{3}}{2} = 2 - \sqrt{3}\\\\
&x^2 + y^2 = \left(2 + \sqrt{3}\right)^2 + \left(2 - \sqrt{3}\right)^2 = (4 + 4\sqrt{3}+3) + (4 - 4\sqrt{3}+3) = 2(4+3)= 14\end{align}$MF#%

(.000216)^1/3
=

216

1/3
10⁶

   =

6 x 6 x 6

1/3
10² x 10² x 10²

   =
6
10²

   =
6
100

   = 0.06

1.5625 = 1.25.

35 + 125 = 17.88

35 + 25 x 5 = 17.88

35 + 55 = 17.88

85 = 17.88

5 = 2.235

80 + 65 = 16 x 5 + 65

   = 45 + 65

   = 105 = (10 x 2.235) = 22.35

Let
x
=
162
128
x

Then x² = 128 x 162

   = 64 x 2 x 18 x 9

   = 8² x 6² x 3²

   = 8 x 6 x 3

   = 144.

x = 144 = 12.

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 = 2² x 3² x 7² x 11² = 213444