Question

rationalise the denominator of √3+√2/5+√2​

Answer 1

${\huge{\underline{\mathfrak{\purple{Solution}}}}}$

Step-by-step explanation:

$\frac{ \sqrt{3} + \sqrt{2} }{5 + \sqrt{2} } \\ = \frac{ \sqrt{ 3} + \sqrt{2} }{5 + \sqrt{2} } \times \frac{ 5 - \sqrt{2} }{5 - \sqrt{2} } \\ = \frac{5 \sqrt{3} - \sqrt{6} + 5 \sqrt{2} - 2 }{ {(5)}^{2} - (\sqrt{2} ) {}^{2} } \\ = \frac{5 \sqrt{3} - \sqrt{6} + 5 \sqrt{2} - 2}{25 - 2} \\ = {\boxed{ \frac{5 \sqrt{3} - \sqrt{6} + 5 \sqrt{2} - 2}{23} }}$

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