Waste less time on Facebook — follow Brilliant.
×

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, 3 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Square both sides, you'll end up with a = b + c Michael Mendrin · 3 years, 3 months ago

Log in to reply

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

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

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

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

\( = \sqrt{b} + \sqrt{c} \) Siddhartha Srivastava · 3 years, 3 months ago

Log in to reply

@Siddhartha Srivastava thanks for this! Kenny Indrajaya · 3 years, 3 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...