Question

1)√2(√2+√3)-√3(2√3+√2) 2)(√5-√2)²+2√2(√5-√2) 3)(√7+√3)(√7-√3) 4)(3+2√2)²-(3-√8)²

Answer 1

$1). \sqrt{2} ( \sqrt{2} + \sqrt{3} )- \sqrt{3} (2 \sqrt{3} + \sqrt{2} ) =2+ \sqrt{6} -6- \sqrt{6} =2-6=-4 \\ 2).( \sqrt{5} - \sqrt{2} )^2+2 \sqrt{2} ( \sqrt{5} - \sqrt{2} )= \\ = \sqrt{5} ^2-2 \cdot \sqrt{5} \cdot \sqrt{2} + \sqrt{2} ^2+2 \sqrt{10} -4=5-2 \sqrt{10} +2+2 \sqrt{10} -4=3 \\ 3).( \sqrt{7} + \sqrt{3} )( \sqrt{7} - \sqrt{3} )=7-3=4$
$4).(3+2 \sqrt{2} )^2-(3- \sqrt{8} )^2=(3+2 \sqrt{2} )^2-(3-2 \sqrt{2} )^2= \\ =3^2+2 \cdot 3 \cdot 2 \sqrt{2} +(2 \sqrt{2} )^2-[3^2-2 \cdot 3 \cdot 2 \sqrt{2} +(2 \sqrt{2} )^2]= \\ =9+12 \sqrt{2} +8-(9-12 \sqrt{2} +8)= \\ =9+12 \sqrt{2} +8-9+12 \sqrt{2} -8=24 \sqrt{2}$