Question

I : Rút gọn

\(A=\sqrt{7-4\sqrt{3}}\)

\(B=\sqrt{19-8\sqrt{3}}\)

\(C=\sqrt{21-4\sqrt{5}}\)

\(D=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{8-2\sqrt{5}}\)

help me !!!

Answer 1

I: Rút gọn

\(A=\sqrt{7-4\sqrt{3}}\\ =\sqrt{4-2\cdot2\cdot\sqrt{3}+3}\\ =\sqrt{\left(2-\sqrt{3}\right)^2}\\ =2-\sqrt{3}\)

\(B=\sqrt{19-8\sqrt{3}}\\ =\sqrt{16-2\cdot4\cdot\sqrt{3}+3}\\ =\sqrt{\left(4-\sqrt{3}\right)^2}\\ =4-\sqrt{3}\)

\(C=\sqrt{21-4\sqrt{5}}\\ =\sqrt{20-2\cdot2\sqrt{5}+1}\\ =\sqrt{\left(2\sqrt{5}\right)^2-2\cdot2\sqrt{5}\cdot1+1}\\ =\sqrt{\left(2\sqrt{5}-1\right)^2}\\ =2\sqrt{5}-1\)

Câu D mình làm chưa ra, sorry :<