Question

evaluate root 2 plus root 3 the whole square plus root 5 minus root 2 the whole square

Answer 1

Answer:

$(\sqrt{2}+\sqrt{3})^2+(\sqrt{5}-\sqrt{2})^2=12+2\sqrt{6}-2\sqrt{10}$

Step-by-step explanation:

The given expression is evaluated by using suitable algebraic identities.

Formula used:

$(a+b)^2=a^2+b^2+2ab\\\\(a-b)^2=a^2+b^2-2ab$

Now,

$(\sqrt{2}+\sqrt{3})^2+(\sqrt{5}-\sqrt{2})^2\\\\=(\sqrt{2})^2+(\sqrt{3})^2+2\sqrt{2}\sqrt{3}+(\sqrt{5})^2+(\sqrt{2})^2-2\sqrt{5}\sqrt{2}\\\\=2+3+2\sqrt{6}+5+2-2\sqrt{10}\\\\=12+2\sqrt{6}-2\sqrt{10}$