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Proof, please?

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
3 years, 10 months ago

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Square both sides, you'll end up with a = b + c

Michael Mendrin - 3 years, 10 months ago

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\( \sqrt{ a + 2\sqrt{bc}} \)

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

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

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

\( = \sqrt{b} + \sqrt{c} \)

Siddhartha Srivastava - 3 years, 10 months ago

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thanks for this!

Kenny Indrajaya - 3 years, 10 months ago

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