Question

simplify and rationalise and find the value of:

Answer 1

Hi friend
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your answer
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$\frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } \\ \\ first \: we \: will \: rationalise \: the \: denominator \\ \\ \frac{( \sqrt{2} + \sqrt{3} )}{(3 \sqrt{2} - 2 \sqrt{3}) } \times \frac{(3 \sqrt{2} + 2 \sqrt{3} ) }{(3 \sqrt{2} + 2 \sqrt{3} )} \\ \\ = > \frac{( \sqrt{2} + \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} )}{(3 \sqrt{2}) {}^{2} - (2 \sqrt{3} ) {}^{2} } \\ \\ = > \frac{6 + 2 \sqrt{6} + 3 \sqrt{6} + 6 }{18 - 12} \\ \\ = > \frac{12 + 5 \sqrt{6} }{6}$
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