Can we write $\sqrt{2}+\sqrt{2}+\sqrt{2}+\sqrt{2}$ as a power of $2$?
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Ref: R9624

Solution

For what value of $x$ is $\sqrt{2}+\sqrt{2}+\sqrt{2}+\sqrt{2}=2^x$ true?

A)$\quad \frac{1}{2}\qquad$ B)$\quad 1\frac{1}{2}\qquad$ C)$\quad 2\frac{1}{2}\qquad$ D)$\quad 3\frac{1}{2}\qquad$ E)$\quad4\frac{1}{2}$

We have that $\sqrt{2}+\sqrt{2}+\sqrt{2}+\sqrt{2}=4\sqrt{2}=2^2\times2^{1/2}=2^{2.5}.$

Thus $x = 2\frac{1}{2}$, and the answer is (C).