Question

Please Rationalise the denominator.


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Answer 1

$\textbf{Given:} \: \frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} }$

$\sf \colorbox{pink} {Solution:}$

$⇒\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} }$

$= \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} }$

$= \frac{(7 \sqrt{3} - 5 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} ) }{(4 \sqrt{3} + 3 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2}) }$

$= \frac{7 \sqrt{3} (4 \sqrt{3} - 3 \sqrt{2}) - 5 \sqrt{2} (4 \sqrt{3} - 3 \sqrt{2}) }{(4 \sqrt{3} {)}^{2} - (3 \sqrt{2} {)}^{2} }$

$= \frac{24 - 21 \sqrt{6} - 2 0 \sqrt{6} + 30}{48 - 18}$

$= \frac{114 - 41 \sqrt{6} }{30}$

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