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**srirahulan** · June 14th 2012, 08:28 AM

$\sqrt{8+2\sqrt{15}}=\sqrt{5+\sqrt{3}}$ prove this one.

**mfb** · June 14th 2012, 08:44 AM

$\sqrt{8+2\sqrt{15}}\approx 3.97$
$\sqrt{5+\sqrt{3}}\approx 2.59$
Tricky to prove that both are equal. Is there a typo somewhere?

And apart from that: Your approach so far? What did you try, what did you find out?

**Reckoner** · June 14th 2012, 08:49 AM

Originally Posted by srirahulan

$\sqrt{8+2\sqrt{15}}=\sqrt{5+\sqrt{3}}$ prove this one.

I think you mean

$\sqrt{8+2\sqrt{15}}=\sqrt5+\sqrt3?$

**HallsofIvy** · June 14th 2012, 08:52 AM

Originally Posted by srirahulan

$\sqrt{8+2\sqrt{15}}=\sqrt{5+\sqrt{3}}$ prove this one.

Prove what? That these are equal? They obviously are not. $\sqrt{8+ 2\sqrt{15}}$ is approximately
3.968 and $\sqrt{5+ \sqrt{3}}$ is approximately 2.595.

**HallsofIvy** · June 14th 2012, 09:10 AM

Originally Posted by Reckoner

I think you mean

$\sqrt{8+2\sqrt{15}}=\sqrt5+\sqrt3?$

Ah! Now that makes sense. srirahulan, observe that both sides are positive numbers and square both sides.

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