Question

Calculați:
a){√(2+√3)+√(2-√3)}²
b)√(4-√7)•√(4+√7)

Answer 1

$a) (\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}})^2= \\\\\\(\sqrt{2+\sqrt{3}})^2+ 2* \sqrt{(2+\sqrt{3})(2-\sqrt{3})}+ (\sqrt{2-\sqrt{3}})^2= \\\\ = 2+ \sqrt{3}+2* \sqrt{4-3}+2 - \sqrt{3}= \\\\ = 2+2+ 2*1= \\\\ = \boxed{6} \\\\\\\\ b) \sqrt{4-\sqrt{7}}* \sqrt{4+\sqrt{7}}= \\\\ = \sqrt{(4-\sqrt{7})(4+\sqrt{7})}= \\\\ = \sqrt{16-7}= \\\\ = \sqrt{9}= \\\\ = \boxed{3}$