Question

Rationalise the denominator
4√3+5√2
_______
4√3+3√3​

Answer 1

Answer:

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$\frac{4 \sqrt{3} \: + \: 5 \sqrt{2} }{4 \sqrt{3} \: + \: 3 \sqrt{3} } = \frac{4 \sqrt{3} \: + \: 5 \sqrt{2} }{4 \sqrt{3} \: + \: 3 \sqrt{3} } \times \frac{4 \sqrt{3} \: - \: 3 \sqrt{3} }{4 \sqrt{3} \: - \: 3 \sqrt{3} } \\ \\ = \frac{4 \sqrt{3} (4 \sqrt{3} - 3 \sqrt{3} ) - 3 \sqrt{3}(4 \sqrt{3} - 3 \sqrt{3} )}{ ({4 \sqrt{3}) }^{2} - {( 3 \sqrt{3} )}^{2} } \\ \\ \frac{48 - 36 - 36 + 27}{48 - 27} \\ \\ \frac{3}{21} = \boxed{ \frac{1}{7} }$

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Answer 2

Answer:

$\frac{1}{7}$

is the answer