Question

7 root 3 - 5 root 2 / root 48 + root 8

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{8} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{2 \times 2 \sqrt{3} + 2 \sqrt{2} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 2 \sqrt{2} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 2 \sqrt{2} } \times \frac{4 \sqrt{3} - 2 \sqrt{2} }{4 \sqrt{3} - 2 \sqrt{2} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{7 \sqrt{3} \times 4 \sqrt{3} - 7 \sqrt{3} \times 2 \sqrt{2} - 5 \sqrt{2} \times 4 \sqrt{3} + 5 \sqrt{2} \times 2 \sqrt{2} }{ {(4 \sqrt{3} )}^{2} - {(2 \sqrt{2} )}^{2} } \\ \\ = \frac{84 - 14 \sqrt{6} - 20 \sqrt{6} + 20 }{48 - 8} \\ \\ = \frac{104 - 34 \sqrt{6} }{40} \\ \\ = \frac{52 - 17 \sqrt{6} }{20}$


Hope this helps!!!!

@Mahak24

Thanks...
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Answer 2

I hope this will help u...