The square of an integer is called a perfect square. If $x$ is a perfect square, the next larger perfect square is
$\textbf{(A) }x+1\qquad \textbf{(B) }x^2+1\qquad \textbf{(C) }x^2+2x+1\qquad \textbf{(D) }x^2+x\qquad \textbf{(E) }x+2\sqrt{x}+1$
Solution by e_power_pi_times_i
Since $x$ is a perfect square, denote $k$ such that $k^2 = x$. Then the next perfect square is $(k+1)^2 = k^2+2k+1$. Substituting back in the equation $k = \sqrt{x}$, the next square is $\boxed{\textbf{(E) }x+2\sqrt{x}+1}$.