- Thread starter
- #1
Albert
Well-known member
- Jan 25, 2013
- 1,225
simplify:
$\sqrt {21-4 \sqrt 5 +8\sqrt 3 - 4\sqrt {15}}$
$\sqrt {21-4 \sqrt 5 +8\sqrt 3 - 4\sqrt {15}}$
good solutionHere is my solution:
\(\displaystyle 21+8\sqrt{3}-4\sqrt{5}-4\sqrt{15}=\)
\(\displaystyle 4+4\sqrt{3}-2\sqrt{5}+4\sqrt{3}+12-2\sqrt{15}-2\sqrt{5}-2\sqrt{15}+5=\)
\(\displaystyle \left(2+2\sqrt{3}-\sqrt{5} \right)^2\)
Hence:
\(\displaystyle \sqrt{21+8\sqrt{3}-4\sqrt{5}-4\sqrt{15}}=2+2\sqrt{3}-\sqrt{5}\)