Question

plz help with this question​

Answer 1

Step-by-step explanation:

$\rm \:(i) \: \frac{1}{ \sqrt{9} - \sqrt{8} } \\ \sf \: Multiplying \: \sqrt{9} + \sqrt{8} \: on \: both\: \: \\ \leadsto \: \frac{ \sqrt{9} + \sqrt{8} }{ (\sqrt{9} - \sqrt{8} )( \sqrt{9} + \sqrt{8} ) } \\ \rm \leadsto \: \frac{ \sqrt{9} + \sqrt{8} }{9 - 8} \\ \rm \leadsto \frac{ \sqrt{9} + \sqrt{8} }{1} \\ \rm \leadsto \: \sqrt{9} + \sqrt{8} \\ \rm \leadsto \: 3 + 2 \sqrt{2}$

$(ii) \rm \: {5}^{ \frac{1}{3} } \times {25}^{ \frac{1}{3} } \\ \twoheadrightarrow \: {5}^{ \frac{1}{3} } \times ( {5})^{2 \times \frac{1}{3} } \\ \twoheadrightarrow {5}^{ \frac{1}{3} } \times {5}^{ \frac{2}{3 } } \\ \twoheadrightarrow {5}^{ \frac{1}{3} + \frac{2}{3} } \{ \rm \: {a}^{b} \times {a}^{c} = {a}^{b + c } \} \\ \twoheadrightarrow {5}^{ \frac{3}{3} } \\ \twoheadrightarrow {5}^{1} \\ \twoheadrightarrow5$

Answer 2

Step-by-step explanation:

$2. \: \: \frac{1}{ \sqrt{9} - \sqrt{8} }$

On rationalizing the denominator,

$\frac{1}{ \sqrt{9} - \sqrt{8} } \times \frac{ \sqrt{9} + \sqrt{8} }{ \sqrt{9} + \sqrt{8} }$

$\frac{ \sqrt{9} + \sqrt{8} }{( \sqrt{9} - \sqrt{8})( \sqrt{9} + \sqrt{8} ) }$

$\frac{ \sqrt{9} + \sqrt{8} }{ {( \sqrt{9}) }^{2} - {( \sqrt{8} )}^{2} }$

$\frac{ \sqrt{9} + \sqrt{8} }{9 - 8}$

$\frac{ \sqrt{9} + \sqrt{8} }{1}$

$3 + \sqrt{8}$

$3. \: \: {(5)}^{ \frac{1}{3} } \times {25}^{ \frac{1}{3} }$

${(5)}^{ \frac{1}{3} } \times {(5}^{2} ) ^{ \frac{1}{3} }$

${(5)}^{ \frac{1}{3} } \times {(5)}^{ \frac{2}{3} }$

${(5)}^{ \frac{1}{3} + \frac{2}{3} }$

${(5)}^{ \frac{1 + 2}{3} }$

${(5)}^{ \frac{ \cancel3}{ \cancel3} }$

$5$

I hope it is helpful