# Prove that any non negative number has a square root [closed]

I am in a real analysis class and am having difficulty with this problem:

prove that any non negative real number has a square root.

## closed as off-topic by Did, user147263, Milo Brandt, Shailesh, John BApr 12 '16 at 0:08

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• The square function is a bijection on the positive reals (because it is continuous and strictly increasing). – Evariste Mar 15 '16 at 15:57
• why the downvotes? – Jens Renders Mar 15 '16 at 16:06

Let $b>0$ and consider the set given by: $$S_b=\{x\in\mathbb{R}:x^2<b\}.$$ Then prove that this set has an upper bound, and that $\alpha=\sup S_b$ satisfies $\alpha^2=b$