Question

Bài tập: Rút gọn biểu thức

a. \(A=\sqrt{5+\sqrt{21}}+\sqrt{5-\sqrt{21}}\)

b. \(B=\sqrt{7+\sqrt{33}}+\sqrt{7-\sqrt{33}}\)

Answer 1

\(A=\sqrt{5+\sqrt{21}}+\sqrt{5-\sqrt{21}}\)

\(A^2=\left(\sqrt{5+\sqrt{21}}^2+2\sqrt{\left(5+\sqrt{21}\right)\left(5-\sqrt{21}\right)}+\sqrt{5-\sqrt{21}}^2\right)\)

\(A^2=5+\sqrt{21}+\sqrt{4\left(5+\sqrt{21}\right)\left(5-\sqrt{21}\right)}+5-\sqrt{21}\)

\(A^2=10+\sqrt{4.\left(25-21\right)}\)

\(A^2=10+\sqrt{4.4}=10+4=14\)

\(A=\sqrt{14}\)

Tương tự

Answer 2

a) 3,7416557387 b) 4,69041576