Question

The expression $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is equivalent to :

• A. $\sqrt{2}$
• B. $2$
• C. $4$
• D. $8$

Answer 1

Answer: (B)

$2$

Given:

$E=\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$

Simplifying it, we get

$\Rightarrow E=\frac{\sqrt{16\times 2}+\sqrt{16\times 3}}{\sqrt{4\times 2}+\sqrt{4\times 3}}$

$\Rightarrow E=\frac{4\sqrt{2}+4\sqrt{3}}{2\sqrt{2}+2\sqrt{3}}=\frac{4(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}=2$

Hence, $E=\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}=2$

Option $B.$