Question

solve

rationalise the denominator ​

Answer 1

Answer:

root 3 /root 2

Step-by-step explanation:

When we multilpy the denominators,we get

(root6)^2-(2)^

6-4

2

Now the numerator is root 2×root 3

So root 2×root 3/2

=root3/root2

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{\boxed { \huge \mathcal\red{\mathcal{Solution}}}}}$

Given:-

$\red{ \implies}\frac{ \sqrt{2} }{ \sqrt{6} - \sqrt{2} } + \frac{ \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \\ \red{ \implies} \frac{ \sqrt{2}( \sqrt{6} + \sqrt{2}) + \sqrt{ 3}( \sqrt{6} - \sqrt{2}) }{( \sqrt{6} - \sqrt{2})( \sqrt{6} + \sqrt{2}) } \\ \red{ \implies} \frac{ \sqrt{2} \times \sqrt{6} + \sqrt{2} \times \sqrt{2} + \sqrt{3} \times \sqrt{6} - \sqrt{2} \times \sqrt{3} }{( \sqrt{6}) {}^{2} - ( \sqrt{2} ) {}^{2} } \\ \red{ \implies} \frac{ \sqrt{12} + 2 + \sqrt{18} - \sqrt{6} }{6 - 2} \\ \red{ \implies} \frac{2 \sqrt{3} + 2 + 3 \sqrt{2} - \sqrt{6} }{4}$

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