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Today my friend gave me a formula which: $$\sqrt{a+2\sqrt{bc}} = \sqrt{b} + \sqrt{c}$$ Where $$b+c=a$$. Can you give me the proof? She got it from her teacher, yet she didn't ask how her teacher got the formula.

Note by Kenny Indrajaya
2 years, 11 months ago

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Square both sides, you'll end up with a = b + c · 2 years, 11 months ago

$$\sqrt{ a + 2\sqrt{bc}}$$

$$= \sqrt{b + c + 2\sqrt{bc}}$$

$$= \sqrt{ (\sqrt{b})^2 + (\sqrt{c})^2 + 2\sqrt{bc}}$$

$$= \sqrt{ (\sqrt{b} + \sqrt{c})^2 }$$

$$= \sqrt{b} + \sqrt{c}$$ · 2 years, 11 months ago