Question

After rationalising the denominator of $\frac{7}{3\sqrt{3}-2\sqrt{2}}$ , we get the denominator as .

Answer 1

Given: $\frac{7}{3\sqrt{3}-2\sqrt{2}}$

Rationalising the denominator,

$=\frac{7(3\sqrt{3}+2\sqrt{2})}{(3\sqrt{3}-2\sqrt{2})(3\sqrt{3}+2\sqrt{2})}$

$=\frac{21\sqrt{3}+14\sqrt{2}}{(3\sqrt{3}{)}^2-(2\sqrt{2}{)}^2}$

$=\frac{21\sqrt{3}+14\sqrt{2}}{27-8}$

$=\frac{21\sqrt{3}+14\sqrt{2}}{19}$

The denominator is $19$.