Question

Rationalise the denominator of
$2 \div \sqrt{7} + \sqrt{5}$
​

Answer 1

${ \textsf{ \textbf{ \large{ \sf{ \color{red}{➣ \: Question : }}}}}}$

• Rationalise the denominator of :–

$\implies \sf \large{ \frac{2}{ \sqrt{7} + \sqrt{5} } }$

${ \textsf{ \textbf{ \large{ \sf{ \color{red}{➣ \: Answer : }}}}}}$

$\circ \: \: { \underline{ \boxed{ \color{violet}{( \sqrt{7} - \sqrt{5} }}}}$

${ \textsf{ \textbf{ \large{ \sf{ \color{red}{➣ \: Solutíon: }}}}}}$

$\sf \underline{to \: rationalise\: } \implies \sf \large{ \frac{2}{ \sqrt{7} + \sqrt{5} } }$

• By rationalising the denominator

$\implies \sf \large{ \frac{2}{ \sqrt{7} + \sqrt{5} } \times \frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} - \sqrt{5}} }$

• using the formula a²- b² = (a - b) (a + b)

$\implies \sf \large{ \frac{2( \sqrt{7} - \sqrt{5} )}{ { \sqrt{7} \: }^{2} - { \sqrt{5} \: }^{2} } }$

$\implies \sf \large{ \frac{2( \sqrt{7} - \sqrt{5} ) }{(7 - 5)}}$

$\implies \sf \large{ \frac{2( \sqrt{7} - \sqrt{5} ) }{(2)}}$

$\implies \sf \large \cancel{ \frac{2( \sqrt{7} - \sqrt{5} ) }{(2)}}$

$\implies { \underline{ \boxed{ \color{green}{( \sqrt{7} - \sqrt{5} }}}}$

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Answer 2

Step-by-step explanation:

${ \textsf{ \textbf{ \large{ \sf{ \color{red}{➣ \: Question : }}}}}}$

Rationalise the denominator of :–

$\implies \sf \large{ \frac{2}{ \sqrt{7} + \sqrt{5} } }$

${ \textsf{ \textbf{ \large{ \sf{ \color{red}{➣ \: Answer : }}}}}}$

$\circ \: \: { \underline{ \boxed{ \color{violet}{( \sqrt{7} - \sqrt{5} }}}}$

${ \textsf{ \textbf{ \large{ \sf{ \color{red}{➣ \: Solutíon: }}}}}}$

$\sf \underline{to \: rationalise\: } \implies \sf \large{ \frac{2}{ \sqrt{7} + \sqrt{5} } }$

By rationalising the denominator

$\implies \sf \large{ \frac{2}{ \sqrt{7} + \sqrt{5} } \times \frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} - \sqrt{5}} }$

using the formula a²- b² = (a - b) (a + b)

$\implies \sf \large{ \frac{2( \sqrt{7} - \sqrt{5} )}{ { \sqrt{7} \: }^{2} - { \sqrt{5} \: }^{2} } }$

$\implies \sf \large{ \frac{2( \sqrt{7} - \sqrt{5} ) }{(7 - 5)}}$

$\implies \sf \large{ \frac{2( \sqrt{7} - \sqrt{5} ) }{(2)}}$

$\implies \sf \large \cancel{ \frac{2( \sqrt{7} - \sqrt{5} ) }{(2)}}$

$\implies { \underline{ \boxed{ \color{green}{( \sqrt{7} - \sqrt{5} }}}}$

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