Question

Rationalise the denominator of:
5√3-4√2/4√3+3√2​

Answer 1

The value is $\frac{84-31\sqrt{6}}{30}$.

Step-by-step explanation:

The expression is:

$\frac{5\sqrt{3}-4\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}$

Rationalise the denominator as follows:

$\frac{5\sqrt{3}-4\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}=\frac{5\sqrt{3}-4\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}\times \frac{4\sqrt{3}-3\sqrt{2}}{4\sqrt{3}-3\sqrt{2}}$

             $=\frac{(5\sqrt{3}-4\sqrt{2})(4\sqrt{3}-3\sqrt{2})}{(4\sqrt{3}+3\sqrt{2})(4\sqrt{3}-3\sqrt{2})}$

             $=\frac{(5\sqrt{3}\times 4\sqrt{3})-(5\sqrt{3}\times 3\sqrt{2})-(4\sqrt{2}\times4\sqrt{3})+(4\sqrt{2}\times3\sqrt{2})}{(4\sqrt{3})^{2}-(3\sqrt{2})^{2}}$

             $=\frac{60-15\sqrt{6}-16\sqrt{6}+24}{48-18}$

             $=\frac{84-31\sqrt{6}}{30}$

Thus, the value is $\frac{84-31\sqrt{6}}{30}$.

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