Question

evaluate (root 5 + 2 root 2)^2 - (root 5 - root 8)^2

Answer 1

\[(\sqrt5+2\sqrt2)^2 - (\sqrt5-\sqrt8)^2= (\sqrt5+2\sqrt2)^2 -(\sqrt5-2\sqrt2)^2=\]
\[= (5 + 4x2 + 2 \times \sqrt5 \times 2 \times \sqrt2) - (5 + 4x2 - 2 \times \sqrt5 \times 2 \times \sqrt2) =\]
\[= 8 \sqrt5 \sqrt 2\]