Question

solve (root5+root2)^2 - (root 8-root3)^2

Answer 1

$( \sqrt{5} + \sqrt{2} ) {}^{2} - ( \sqrt{8} - \sqrt{3} ) {}^{2} \\ = (5 + 2 + 2 \sqrt{10} ) - (8 + 3 - 2 \sqrt{24} ) \\ = (7 + 2 \sqrt{10} ) - (11 - 2 \sqrt{6} ) \\ = 7 + 2 \sqrt{10} - 11 + 2 \sqrt{6} \\ = 2( \sqrt{10} + \sqrt{6} ) - 4$

Answer 2

Step-by-step explanation:

$\begin{lgathered}( \sqrt{5} + \sqrt{2} ) {}^{2} - ( \sqrt{8} - \sqrt{3} ) {}^{2} \\ = (5 + 2 + 2 \sqrt{10} ) - (8 + 3 - 2 \sqrt{24} ) \\ = (7 + 2 \sqrt{10} ) - (11 - 2 \sqrt{6} ) \\ = 7 + 2 \sqrt{10} - 11 + 2 \sqrt{6} \\ = 2( \sqrt{10} + \sqrt{6} ) - 4\end{lgathered}$