Question

Решите 24, пожалуйста подробно.

Answer 1

√(18√2 - 12√3) = √(6(3√2 - 2√3)) = (6(3√2 - 2√3))^(1/2) = (6(3√2 - 2√3))^(2/4) = ((6(3√2 - 2√3))^2)^(1/4) = (36(9*2 -2*3*2√(2*3) + 4*3))^(1/4) = (36(18 -12√6 + 12))^(1/4) = (36(30 -12√6))^(1/4) = (36*6(5 -2√6))^(1/4) = (216((5 -2√6))^(1/4)


(6((5 + 2√6))^(1/4) * (216((5 -2√6))^(1/4) =
(216*6(5 +2√6)(5 -2√6))^(1/4) =
(1296(25 - 4*6))^(1/4) =
(1296(25 - 24))^(1/4) =
(1296*1)^(1/4) =
(1296)^(1/4) = (216*6)^(1/4) = (36*6*6)^(1/4) = (6*6*6*6)^(1/4) = 6