Question

please solve this by rationalising the denominator​

Answer 1

$\huge \fbox \pink{Solution:}$

$\textbf{Given:} \frac{ \sqrt{2} }{ \sqrt{6} \times \sqrt{2} } + \frac{ \sqrt{3} }{ \sqrt{6} + \sqrt{2} }$

Solve:

$\frac{ \sqrt{2} }{ \sqrt{6} \times \sqrt{2} } + \frac{ \sqrt{3} }{ \sqrt{6} + \sqrt{2} } = \frac{ \sqrt{2}( \sqrt{6} + \sqrt{2} - \sqrt{3} \sqrt{6} - \sqrt{2} )}{( \sqrt{6} - \sqrt{2} )( \sqrt{6} + \sqrt{2}) }$

$= \frac{ \sqrt{12} + 2 - \sqrt{18} + \sqrt{6} }{6 - 2}$

$= \frac{2 \sqrt{3} + 2 - 3 \sqrt{2} + \sqrt{6} }{4}$

$= \frac{2 \sqrt{3} + \sqrt{6} + 2 - 3 \sqrt{2} }{4}$

$\\ \\ \\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$