DXC Quants Surds & Indices Quiz 1

Explanation:
(\sqrt{12} + \sqrt{18}) - (\sqrt{3} + \sqrt{2} )
(2\sqrt{3} - \sqrt{3}) - (3\sqrt{2} - \sqrt{2} )
\sqrt{3} + 2\sqrt{2}

Explanation:
8^{ \frac{2}{3}}= (2^{3)})^{ \frac{3}{2}}
2^{3* \frac{3}{2}}= 2^{2} = 4

Explanation:

Expression = (256)^{0.16} \times (16)^{0.18}
= (4)^{4}\times 0.16 \times (4)^{2}\times 0.18
= (4)^{0.64}\times (4)^{0.36}
= (4)^{0.64+0.36}
= (4)^{1} = 4

Explanation:
= 2 + 0.3 - 0.2 ´-75/100 *2.80
= 2.3 – 0.2 – 2.1
= 2.3 – 2.3 = 0

Explanation:

Expression = (0.04)^{–1.5}
= \frac{1}{ 0.04^{1.5} = \frac{1}{ 0.04^{\frac{3}{2}}
= \frac{1}{(0.04 *0.04*0.04)^{\frac{1}{2}}}
= \frac{1}{\sqrt{0. 0000064}}
= \frac{1}{0.008} =\frac{1000}{8}= 125

Explanation:

(243)^{0.16} \times (243)^{0.04}
= (243)^{0.16} + 0.04
= (243)^{0.2} = (243)^{\frac{1}{5}}
= (3^{5})^{\frac{1}{5}} = 3

Explanation:

Expression = 3^{0} + \frac{3^{-1}}{3^{-1}} - 3^{0}
\frac{1 +\frac{1}{3}}{\frac{1}{3} -1} = \frac{\frac{(3+1)}{3} }{\frac{(1-3)}{3}}
\frac{4}{3} \times -\frac{3}{2}
= –2

Explanation:

(256)^\frac{16}{100} \times (256)^\frac{9}{100}
= (256)^{\frac{25}{100}} = (256)^{\frac{1}{4}}
= (4^{4})^{\frac{1}{4}} [/atex]<br /> =( 4)^{4\times \frac{1}{4}} = 4

Explanation:

(4)^0.5 \times (0.5)^4
= (2^{2})^{\frac{1}{2}) \times(\frac{5}{10})^{4}}
= 2 \times (\frac{1}{2})^{4}
= \frac{2}{2} \times 2 \times2 \times 2 = \frac{1}{8}

Explanation:

=(256) ^{-4 ^{\frac{3}{2}}} = (256) ^{\frac{1}{4} ^{\frac{3}{2}}}
=(256) ^{-\frac{1}{8}} =\frac{1}{(256) ^{\frac{1}{8}} }
= \frac{1}{(2 ^{8})^{\frac{1}{8}}} =\frac{1}{2}