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

4a² - 4a + 1 + 3a = (1)² + (2a)² - 2 x 1 x 2a + 3a

   = (1 - 2a)² + 3a

   = (1 - 2a) + 3a

   = (1 + a)

   = (1 + 0.1039)

   = 1.1039

Answer : Option C

Explanation :

$MF#%\text{Difference = }(\sqrt{18}+\sqrt{3}) - (\sqrt{2}+\sqrt{12})\\\
= (\sqrt{2 \times 9}+\sqrt{3}) - (\sqrt{2}+\sqrt{3 \times 4})\\\\
= (3\sqrt{2}+\sqrt{3}) - (\sqrt{2}+2\sqrt{3}) \\\\
= 3\sqrt{2}+\sqrt{3} -\sqrt{2} - 2\sqrt{3}\\\\
= 2\sqrt{2} - \sqrt{3}$MF#%

Answer : Option C

Explanation :

$MF#%\sqrt[3]{4\dfrac{12}{125}}=\sqrt[3]{\dfrac{512}{125}} = \sqrt[3]{\dfrac{2\times 2 \times 2 \times 2\times 2 \times 2 \times 2\times 2 \times 2}{5 \times 5 \times 5}} =\dfrac{2\times 2 \times 2 }{5} = \dfrac{8}{5} = 1\dfrac{3}{5}$MF#%

Answer : Option A

Explanation :

$MF#%\dfrac{x}{\sqrt{512}} = \dfrac{\sqrt{648}}{x}\\\\
\Rightarrow x^2 = \sqrt{512} \times \sqrt{648} = \sqrt{512 \times 648}
= \sqrt{2 \times 2 \times 2 \times 64 \times 2 \times 2 \times 2 \times 81 } = 2\times 2 \times 2 \times 8 \times 9 \\\\
x = \sqrt{2\times 2 \times 2 \times 8 \times 9} = 2 \times 4 \times 3 = 24$MF#%

To make it a perfect cube, it must be multiplied by 5.

Answer : Option B

Explanation :

$MF#%8+2\sqrt{15}= 5+3 + 2 \times\sqrt{5} \times \sqrt{3}
\\\\=(\sqrt{5})^2+(\sqrt{3})^2 + (2 \times\sqrt{5} \times \sqrt{3})
\\\\= (\sqrt{5} +\sqrt{3} )^2$MF#%

$MF#%\text{Hence, }\sqrt{\left(8+2\sqrt{15}\right)} = \sqrt{(\sqrt{5} +\sqrt{3} )^2} = \sqrt{5} +\sqrt{3} $MF#%

Answer : Option D

Explanation :

$MF#%\sqrt{248 + \sqrt{64}} = \sqrt{248 +8} = \sqrt{256} = 16$MF#%

Answer : Option C

Explanation :

$MF#%\sqrt{4a^2 - 4a + 1 } + 3a = \sqrt{(1)^2 - 2 \times 1 \times 2a + (2a)^2} + 3a = \sqrt{\left(1 -2a\right)^2}+ 3a \\\\= 1 - 2a + 3a = 1 + a\\\\
=1 + 0.2917 = 1.2917$MF#%