Question

Ans the sum step by step in photo

Answer 1

Answer:

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$The \: answer \: is \: = \sqrt{3} + \frac{1}{ \sqrt{5} }$

Step-by-step explanation:

Given:-

• $\frac{14}{5 \sqrt{3} - \sqrt{5} }$

To Find:-

• Rationalize the Denominator!

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$\frac{14}{5 \sqrt{3} - \sqrt{5} } \\ \\ Rationalize \: the \: denominator \\ \\ = > \frac{14}{5 \sqrt{3} - \sqrt{5} } \times \frac{{5 \sqrt{3} + \sqrt{5} }}{{5 \sqrt{3} + \sqrt{5} }} \\ \\ = > \frac{14(5 \sqrt{3} + \sqrt{5} )}{ [ {(5 \sqrt{3}) }^{2} - {( \sqrt{5} )}^{2} ] } \\ \\ = > \frac{14( 5\sqrt{3} + \sqrt{5} ) }{25 \times 3 - 5} \\ \\ = > \frac{14 (5\sqrt{3} + \sqrt{5} ) }{75 - 5} \\ \\ = > \frac{14(5 \sqrt{3} + \sqrt{5} )}{70} \\ \\ = > Cut \: 70 \: with \: 14 \: \: \: we \: have \\ \\ = > \frac{5 \sqrt{3} + \sqrt{5} }{5} \\ \\ = > \frac{5 \sqrt{3} }{5} + \frac{ \sqrt{5} }{5} \\ \\ = > \sqrt{3} + \frac{ \sqrt{5} }{ {( \sqrt{5} )}^{2} } \\ \\ = > \sqrt{3} + \frac{1}{ \sqrt{5} }$

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