Question

Rationalize the following 4√3 +5√2 upon √48 + √18

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{4 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ \\ = \frac{4 \sqrt{3} + 5\sqrt{2} }{2 \times 2 \sqrt{3} + 3 \sqrt{2} } \\ \\ = \frac{4 \sqrt{3} + 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \\ \\ = \frac{4 \sqrt{3} + 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{4 \sqrt{3} \times 4 \sqrt{3} - 4 \sqrt{3} \times 3 \sqrt{2} + 5 \sqrt{2} \times 4 \sqrt{3} - 5 \sqrt{2} \times 3 \sqrt{2} }{ {(4 \sqrt{3}) }^{2} - {(3 \sqrt{2} )}^{2} } \\ \\ = \frac{48 - 12 \sqrt{6} + 20 \sqrt{6} - 30 }{48 - 18} \\ \\ = \frac{18 + 8 \sqrt{6} }{30} \\ \\ = \frac{9 + 4 \sqrt{6} }{15}$

Hope this helps!!!!

@Mahak24

Thanks...
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