Question

Show that √[5+√15+(√(24+6√15)] = √3+√5

Answer 1

Step-by-step explanation:

$\sqrt{5+\sqrt{15}+\sqrt{24+6\sqrt{15}}}=\sqrt{3}+\sqrt{5}$

Square both sides:

$5+\sqrt{15}+\sqrt{24+6\sqrt{15}}=3+2\sqrt{15}+5$

Rearrange:

$\sqrt{24+6\sqrt{15}}=3+\sqrt{15}$

Square both sides:

$24+6\sqrt{15}=9+6\sqrt{15}+15$

Rearrange:

$0=0$

QED