393. Упростите выражение: a) √7+4√3; б) √6-2√5; в) √5+2√6; г) √3-√8.

a) $$sqrt{7+4sqrt{3}} = sqrt{4 + 4sqrt{3} + 3} = sqrt{(2+sqrt{3})^2} = |2 + \sqrt{3}| = 2 + sqrt{3}$$

б) $$sqrt{6-2sqrt{5}} = sqrt{5 - 2sqrt{5} + 1} = sqrt{(sqrt{5} - 1)^2} = |\sqrt{5} - 1| = sqrt{5} - 1$$

в) $$sqrt{5+2sqrt{6}} = sqrt{2 + 2sqrt{6} + 3} = sqrt{(sqrt{2} + sqrt{3})^2} = |sqrt{2} + \sqrt{3}| = \sqrt{2} + sqrt{3}$$

г) $$sqrt{3 - sqrt{8}} = sqrt{3 - 2sqrt{2}} = sqrt{2 - 2sqrt{2} + 1} = sqrt{(sqrt{2} - 1)^2} = |\sqrt{2} - 1| = sqrt{2} - 1$$