Question

Calculați (√3+2)²-√12
(√45-√5)²-20

Answer 1

     
[tex]1) \\ ( \sqrt{3}+2)^2- \sqrt{12} = \\ = (\sqrt{3})^2 + 2\times \sqrt{3} \times 2 + 2^2 - \sqrt{4 \times 3}= \\ = 3 + 4\sqrt{3} + 4 - 2\sqrt{3}= \boxed{7+2\sqrt{3}} \\ \\ 2) \\ ( \sqrt{45}- \sqrt{5})^2-20 = \\ =( \sqrt{9 \times 5}- \sqrt{5})^2-20 = \\ =( 3\sqrt{5}- \sqrt{5})^2-20 = \\ =(2 \sqrt{5})^2-20 = \\ =2^2 \times (\sqrt{5})^2-20 = \\ =4 \times 5 -20 = 20-20 = \boxed{0} [/tex]