Question

Rút Gọn :

a) \(A=\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)

b) \(B=\sqrt[3]{9}.\sqrt[3]{-3}+\left(1+\sqrt{2}\right)^2\)

Answer 1

\(A=\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)

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

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

\(=\left|\sqrt{5}-2\right|-\left|\sqrt{5}+2\right|\)

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

\(=-4\)

Answer 2

\(B=\sqrt[3]{9}.\sqrt[3]{-3}+\left(1+\sqrt{2}\right)^2\)

\(=-\sqrt[3]{27}+3+2\sqrt{2}\)

\(=-3+3+2\sqrt{2}\)

\(=2\sqrt{2}\)