1. ## fix IT

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

2. ## Re: fix IT

$\displaystyle \sqrt{8+2\sqrt{15}}\approx 3.97$
$\displaystyle \sqrt{5+\sqrt{3}}\approx 2.59$
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?

3. ## Re: fix IT

Originally Posted by srirahulan
$\displaystyle \sqrt{8+2\sqrt{15}}=\sqrt{5+\sqrt{3}}$ prove this one.
I think you mean

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

4. ## Re: fix IT

Originally Posted by srirahulan
$\displaystyle \sqrt{8+2\sqrt{15}}=\sqrt{5+\sqrt{3}}$ prove this one.
Prove what? That these are equal? They obviously are not. $\displaystyle \sqrt{8+ 2\sqrt{15}}$ is approximately
3.968 and $\displaystyle \sqrt{5+ \sqrt{3}}$ is approximately 2.595.

5. ## Re: fix IT

Originally Posted by Reckoner
I think you mean

$\displaystyle \sqrt{8+2\sqrt{15}}=\sqrt5+\sqrt3?$
Ah! Now that makes sense. srirahulan, observe that both sides are positive numbers and square both sides.