Question

Rationalise 4√3 + 5√2/4√8 + √18

Answer 1

ANSWER:--------

$\rm given : - \frac{4 \sqrt{3} + 5 \sqrt{2} }{4 \sqrt{8} + \sqrt{18} } \\ \\ \rm now \: \sqrt{8} \: can \: be \: written \: as = 2 \sqrt{2} \\ \rm similarly \: \sqrt{18} = 3 \sqrt{2} \\ \\ \rm = \frac{4 \sqrt{3} + 5 \sqrt{2} }{(4 \times 2 \sqrt{2} ) + 3 \sqrt{2} } \\ \\ \rm = \frac{4 \sqrt{3} + 5 \sqrt{2} }{8 \sqrt{2} + 3 \sqrt{2} } \\ \\ \rm = \frac{4 \sqrt{3} + 5 \sqrt{2} }{11 \sqrt{2} } \times \frac{11 \sqrt{2} }{11 \sqrt{2} } \\ \\ \rm = \frac{11 \sqrt{2}(4 \sqrt{3} + 5 \sqrt{2}) }{11 \sqrt{2} \times 11 \sqrt{2} } \\ \\ \rm = \frac{44 \sqrt{6} + 55 \sqrt{4} }{242}$

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