Question

упростить выражения:

1) 4√2+√50-√18

2) √3*(2√3+√12)

3) (√5-2)²

4) (√3-√2)(√3+√2)

Answer 1

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

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

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

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