Question

Выражения: 1) 4√2+√50-√18 2) √3*(2√3+√12) 3) (√5-2)² 4) (√3-√2)(√3+√2)

Answer 1

$1)$
$4 \sqrt{2} +\sqrt{50} -\sqrt{18} =4 \sqrt{2} +\sqrt{25*2} -\sqrt{9*2} =4 \sqrt{2} +5\sqrt{2} -3\sqrt{2} =6 \sqrt{2}$

$2)$
$\sqrt{3}* (2 \sqrt{3} + \sqrt{12})= \sqrt{3}* (2 \sqrt{3} +2 \sqrt{3})= \sqrt{3} *4 \sqrt{3} =3*4=12$

$3)$
$( \sqrt{5} -2)^2=( \sqrt{5} )^2+2^2-2*2* \sqrt{5} =5+4-4 \sqrt{5}=9-4 \sqrt{5}$

$4)$
$( \sqrt{3}- \sqrt{2}) ( \sqrt{3}+ \sqrt{2}) =( \sqrt{3})^2-( \sqrt{2})^2=3-2=1$