Question

Varun was facing some difficulty in simplyfying $\frac{1}{\sqrt{7}-\sqrt{3}}.$ His classmate Priya gave him a clue to rationalise the denominator for simplification. Varun Simplified the expression and thanked Priya for this good will. How Varun simplified $\frac{1}{\sqrt{7}-\sqrt{3}}.$? What value does it indicate?

Answer 1

The rationalising factor for $\frac{1}{\sqrt{7}-\sqrt{3}}$ is $\sqrt{7}+\sqrt{3}$. So
$$\begin{gathered} \frac{1}{\sqrt{7}-\sqrt{3}}=\frac{\sqrt{7}+\sqrt{3}}{\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)} \\ =\frac{\sqrt{7}+\sqrt{3}}{{\left(\sqrt{7}\right)}^2-{\left(\sqrt{3}\right)}^2} \\ =\frac{\sqrt{7}+\sqrt{3}}{7-3} \\ =\frac{1}{4}\left(\sqrt{7}+\sqrt{3}\right) \end{gathered}$$
Varun simplified $\frac{1}{\sqrt{7}-\sqrt{3}}$ by multiplying the numerator and denominator by $\sqrt{7}+\sqrt{3}$.
It indicates the value of co-operation and help.