Does the square root of 2 exist?

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If I interpret your question as a straightforward mathematical question--Is there a number whose square is 2?--then the answer is of course yes. The numerical value of the number is approximately 1.41421.

But perhaps that isn't what you meant. Perhaps your question is about the sense in which mathematical objects like numbers exist. Do they really exist (whatever that means), or are they just, in some sense, figments of our imaginations? You might want to look at the answers to question 139, and also the links to the Stanford Encyclopedia in those answers, for a discussion of two different ways that people have interpreted mathematical existence, namely platonism and intuitionism. It is perhaps worth mentioning that both a platonist and an intuitionist would agree that the square root of 2 exists, but they would mean different things by that. The platonist would mean that the square root of 2 is one of the objects in a world of mathematical objects that exists independent of us and our mathematical activities. The intuitionist would mean something like "I know how to compute, to any desired degree of accuracy, a number whose square is 2."

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