Question

Найдите значение выражения:
а) (1-2√3)(1+2√3)
б) (3√12+2√3)^2
в) √(3-2√5)^2 все выражение под корнем
г) √75-(√6-2√2)*√2-3√3
д) (5√3-√108+√21)*√3-3√7

Answer 1

$1)(1-2sqrt{3})(1+2sqrt{3})=1^{2} -(2sqrt{3})^{2}=1-12=-11\\2)(3sqrt{12}+2sqrt{3})^{2}=(3sqrt{4*3}+2sqrt{3})^{2}=(6sqrt{3}+2sqrt{3})^{2}=(8sqrt{3} )^{2}=64*3=192\\3)sqrt{(3-2sqrt{5})^{2}} =|3-2sqrt{5}|=2sqrt{5}-3$$4)sqrt{75}-(sqrt{6} -2sqrt{2})*sqrt{2}-3sqrt{3}=sqrt{25*3}-sqrt{6*2}+2sqrt{2}*sqrt{2}-3sqrt{3}=5sqrt{3}-2sqrt{3}+4-3sqrt{3}=4$$5)(5sqrt{3}-sqrt{108}+sqrt{21} )*sqrt{3}-3sqrt{7}=(5sqrt{3}-sqrt{36*3}+sqrt{7*3})*sqrt{3}-3sqrt{7}=5sqrt{3}*sqrt{3}-6sqrt{3}*sqrt{3}+sqrt{7*3*3}-3sqrt{7}=15-18+3sqrt{7}-3sqrt{7}=-3$