Question

rationalize the denominator 5/√3-√2

Answer 1

Correct Question :-

Rationalise the denominator —

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

Correct Answer :-

The required solution is below;

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

$\to \: \frac{5\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}$

$\to \: \frac{5\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$

$\to \: \frac{5\left(\sqrt{3}+\sqrt{2}\right)}{3-2}$

$\to \: \frac{5\left(\sqrt{3}+\sqrt{2}\right)}{1}$

$\to \: 5\left(\sqrt{3}+\sqrt{2}\right)$

$\to \: 5\sqrt{3}+5\sqrt{2}$

∴ Hence, the required rationalization of $\frac{5}{ \sqrt{3} - \sqrt{2} }$ will be $5\sqrt{3}+5\sqrt{2}$.