Question

The square root of$\sqrt{50}+\sqrt{48}$ is

• A. $2^{1/4}(3+\sqrt{2})$
• B. $2^{1/4}(\sqrt{3}+\sqrt{2})$
• C. $2^{1/4}(2+\sqrt{2})$
• D. $2^{1/4}(\sqrt{3}+2)$

Answer 1

Answer: (B)

Now, $\sqrt{50}+\sqrt{48}=5\sqrt{2}+4\sqrt{3}$
$=\sqrt{2}[5+2\cdot \sqrt{2}\cdot \sqrt{3}]$
$=\sqrt{2}(\sqrt{3}+\sqrt{2}{)}^2$
$\therefore \sqrt{\sqrt{50}+\sqrt{48}}$
$=2^{1/4}(\sqrt{3}+\sqrt{2})$