1979 AHSME Problems/Problem 7

Problem 7

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

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 $\boxed{\textbf{(E) }x+2\sqrt{x}+1}$ .

1979 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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1979 AHSME Problems/Problem 7

Problem 7

Solution

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