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Number theory Difficulty 3.0 AMC 10/12 Prove it Canada

Three positive integers $a$ , $b$ and $x$ form an O'Hara triple $(a, b, x)$ if $\sqrt{a} + \sqrt{b} = x$ . For example, $(1, 4, 3)$ is an O'Hara triple because $\sqrt{1} + \sqrt{4} = 3$ . If $(36, 25, x)$ is an O'Hara triple, determine the value of $x$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.