Q75 / 200 · Manipal (MET) 2011 · Mathematics

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

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

Solution

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

Hence, the correct answer is option: 'B'.

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