Robert Bosch Surds and 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

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Explanation:

(256)^\frac{16}{100} \times (256)^\frac{9}{100}

= (256)^{\frac{25}{100}} = (256)^{\frac{1}{4}}

 = (4^{4})^{\frac{1}{4}} [/atex]</span><br /> <br /> <span style="font-weight: 400;">=( 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}