Question

$(\sqrt{5} - 2)(\sqrt{5}+2) - \sqrt{2-\sqrt{3}} + \sqrt{2+\sqrt{3}}$
$(3\sqrt{2} - 2\sqrt{3}) * (\sqrt{18}+ \sqrt{12}) : (\sqrt{75} - \sqrt{27})$$[(\sqrt{2}-\sqrt{3})^2 - (2\sqrt{2} - \sqrt{3})^2] * (6+2\sqrt{6}) + 12$

Answer 1

√(2-√3)=√[(2+√(4-3)]/2-√[(2-√(4-3)]/2=√(2+1)/2-√(2-1)/2=√3/√2-1/√2=√6/2-√2/2
√(2+√3)=√[(2+√(4-3)]/2+√[(2-√(4-3)]/2=√(2+1)/2+√(2-1)/2=√3/√2+1/√2=√6/2+√2/2
(√5-2)(√5+2)-√(2-√3)+√(2+√3)=
=(5-4)-√6/2+√2/2+√6/2+√2/2=
=1+√2

(3√2-2√3)*(√18+√12) :(√75-√27)=
=(3√2-2√3)*(3√2+2√3) :(5√3-3√3)=
=(18-12) :(2√3)=
=6/2√3=3/√3=3√3/3=√3

[(√2-√3)²-(2√2-√3)²] *(6+2√6)+12=
=[(2-2√6+3-8+4√6-3)]*(6+2√6)+12=
=(2√6-6)*(2√6+6)+12=
=(24-36)+12=
=-12+12=0