Question

Find the value of $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}.$

• A. $\frac{2}{\sqrt{2}+\sqrt{3}}$
• B. $\sqrt{2}+\sqrt{3}$
• C. $2$
• D. $1$

Answer 1

The correct option is C $2$

$\left(\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}\right)=\left(\frac{\sqrt{16\times 2}+\sqrt{16\times 3}}{\sqrt{4\times 2}+\sqrt{4\times 3}}\right)\left(\frac{4\sqrt{2}+4\sqrt{3}}{2\sqrt{2}+2\sqrt{3}}\right)=\left(\frac{4}{2}\right)\left(\frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)=2$