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