Question

Упростите выражения $(2-sqrt{3})*sqrt{7+4sqrt{3}}$

Answer 1

$(2-sqrt{3})*sqrt{7+4sqrt{3}}=\\(2-sqrt{3})*sqrt{4+4sqrt{3}+3}=\\(2-sqrt{3})*sqrt{2^2+2*2*sqrt{3}+(sqrt{3})^2}=\\(2-sqrt{3})*sqrt{(2+sqrt{3})^2}=\\(2-sqrt{3})*|2+sqrt{3}|=\\(2-sqrt{3})*(2+sqrt{3})=\\2^2-(sqrt{3})^2=\\4-3=1$