Question

Two classmates Salma and Anil siplified two different expressions during the revision hour and explained to each other their simplification. Salma explains simplification of $\frac{\sqrt{2}}{\sqrt{5}+\sqrt{3}}$ and Anil explains simplification of $\sqrt{28}+\sqrt{98}+\sqrt{147}$. Write both the simplifications. What value does it depict?

Answer 1

Salma's expression

$\frac{\sqrt{2}}{\sqrt{5}+\sqrt{3}}\times \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ [By using Rationalization].

$=\frac{\sqrt{2}(\sqrt{5}-\sqrt{3})}{(\sqrt{5}{)}^2-(\sqrt{3}{)}^2}$

$=\frac{\sqrt{10}-\sqrt{6}}{2}$.

Anil's expression

$\sqrt{28}+\sqrt{98}+\sqrt{147}$

$=\sqrt{7\times 4}+\sqrt{49\times 2}+\sqrt{49\times 3}$

$=2\sqrt{7}+7\sqrt{2}+7\sqrt{3}$

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