Question

4√3+5√2 /√ 48+√18 rationalize the denominator

Answer 1

hope this answer will help you.

Answer 2

Answer:

$\\ \sf \: \frac{4 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{2 \times 2 \times 2 \times 2 \times 3} + \sqrt{3 \times 3 \times 2} } \\ \\ \\ \implies \sf \: \frac{4 \sqrt{3} + 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} }$

RF = 4√3 - 3√2

$\large{ \underline{ \mathrm{ \green{multiply \: \: and \: \: divide \: \: by \: \: Rf \: \: }}}} \\ \\ \\ \implies \sf \: \frac{4 \sqrt{3} + 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \\ \\ \\ \implies \sf \: \frac{4 \sqrt{3} \: ( \: 4 \sqrt{3} - 3 \sqrt{2} ) + 5 \sqrt{2} \: ( \: 4 \sqrt{3} - 3 \sqrt{2} ) }{(4 \sqrt{3}) {}^{2} - (3 \sqrt{2} ) {}^{2} } \\ \\ \\ \implies \sf \: \frac{48 - 12 \sqrt{6} + 20 \sqrt{6} - 30 }{48 - 18} \\ \\ \\ \implies \sf \: \frac{48 - 30 - 12 \sqrt{6} + 20 \sqrt{6} }{30} \\ \\ \\ \implies \sf \: \frac{18 + 8 \sqrt{6} }{30} \\ \\ \\ \implies \sf \blue{ \frac{9 + 4 \sqrt{6} }{15} }$