Question

What denominator do we obtain after rationalizing the denominator of $\frac{4}{7\sqrt{5}-5\sqrt{7}}$?

Answer 1

To find: Denominator after rationalising the fraction $\frac{4}{7\sqrt{5}-5\sqrt{7}}$

$=\frac{4}{7\sqrt{5}-5\sqrt{7}}\times \frac{7\sqrt{5}+5\sqrt{7}}{7\sqrt{5}+5\sqrt{7}}=\frac{22\sqrt{5}+20\sqrt{7}}{(7\sqrt{5}{)}^2-(5\sqrt{7}{)}^2}$ $\left[\right(a+b\left)\right(a-b)=a^2-b^2]$

$=\frac{28\sqrt{5}+20\sqrt{7}}{245-175}=\frac{28\sqrt{5}+20\sqrt{7}}{70}$

Denominator after rationalising $=70$.