If $n>0$ and $\sqrt{n^{2}+n^{2}+n^{2}+n^{2}}=64$, then $n$ equals
(A) $\sqrt{8}$
(B) 16
(C) 4
(D) 32
(E) $\sqrt{2}$
Solution 1

Since $\sqrt{n^{2}+n^{2}+n^{2}+n^{2}}=64$, then $\sqrt{4 n^{2}}=64$ or $2 n=64$, since $n>0$.

Thus, $n=32$.

## Solution 2

Since $\sqrt{n^{2}+n^{2}+n^{2}+n^{2}}=64$, then $\sqrt{4 n^{2}}=64$.

Thus, $4 n^{2}=64^{2}=4096$, and so $n^{2}=1024$.

Since $n>0$, then $n=\sqrt{1024}=32$.

ANSWER: (D)