Question

Rationalized the denominator $\frac{1}{\sqrt{3}-\sqrt{2}},\frac{1}{3\sqrt{2}},\frac{1}{\sqrt{3}}$

Answer 1

Rationalizing the denominator of $\frac{1}{\sqrt{3}-\sqrt{2}}$.

$\frac{1}{\sqrt{3}-\sqrt{2}}\times \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

$=\frac{\sqrt{3}+\sqrt{2}}{{\left(\sqrt{3}\right)}^2-{\left(\sqrt{2}\right)}^2}$

$=\frac{\sqrt{3}+\sqrt{2}}{3-2}$

$=\sqrt{3}+\sqrt{2}$

Rationalizing the denominator of $\frac{1}{3\sqrt{2}}$.

$\frac{1}{3\sqrt{2}}\times \frac{3\sqrt{2}}{3\sqrt{2}}$

$=\frac{3\sqrt{2}}{{\left(3\sqrt{2}\right)}^2}$

$=\frac{3\sqrt{2}}{18}$

$=\frac{\sqrt{2}}{6}$

Rationalizing the denominator of $\frac{1}{\sqrt{3}}$.

$\frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}$

$=\frac{\sqrt{3}}{{\left(\sqrt{3}\right)}^2}$

$=\frac{\sqrt{3}}{3}$