Competition problem — Number theory

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Number theory Difficulty 4.5 AIME Find the answer

9. If $a$ is a perfect square, then the smallest perfect square greater than $a$ is $\qquad$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

The smallest perfect square greater than $a$ is
$(\sqrt{a}+1)^{2}=a+2 \sqrt{a}+1 .$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.