Question

$\sqrt{\sqrt{50}+\sqrt{48}}=k(\sqrt{3}+\sqrt{2})$, then $k=$........

• A. $2^{1/2}$
• B. $2^{1/4}$
• C. $2$
• D. $2^{1/8}$

Answer 1

Answer: (B)

The correct option is C $2^{1/4}$

$\sqrt{\sqrt{50}+\sqrt{48}}=k(\sqrt{3}+\sqrt{2})$

On squaring both sides,

$\sqrt{50}+\sqrt{48}=k^2(\sqrt{3}+\sqrt{2}{)}^2$

$\sqrt{50}+\sqrt{48}=k^2(3+2+2\sqrt{6})$

$5\sqrt{2}+4\sqrt{3}=k^2(5+2\sqrt{6})$

$\sqrt{2}(5+2\sqrt{2}\sqrt{3})=k^2(5+2\sqrt{6})$

$\sqrt{2}(5+2\sqrt{6})=k^2(5+2\sqrt{6})$

$k^2=\sqrt{2}$

$k=2^{1/4}$