Question

Thực hiện phép tính (rút gọn biểu thức) 

a)\(\left(\sqrt{3}-2\right)\sqrt{7+4\sqrt{3}}\)

b) \(\sqrt{6+\sqrt{32}}\) - \(\sqrt{11-\sqrt{72}}\)

c) \(\sqrt{21-4\sqrt{5}}\) + \(\sqrt{21+4\sqrt{5}}\)

Answer 1

a: \(=\left(\sqrt{3}-2\right)\cdot\sqrt{\left(2+\sqrt{3}\right)^2}\)

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

=3-4=-1

b: \(=\sqrt{6+4\sqrt{2}}-\sqrt{11-2\sqrt{18}}\)

\(=\sqrt{\left(2+\sqrt{2}\right)^2}-\sqrt{\left(3-\sqrt{2}\right)^2}\)

\(=2+\sqrt{2}-3+\sqrt{2}=2\sqrt{2}-1\)

c: \(=\sqrt{\left(2\sqrt{5}-1\right)^2}+\sqrt{\left(2\sqrt{5}+1\right)^2}\)

\(=2\sqrt{5}-1+2\sqrt{5}+1\)

\(=4\sqrt{5}\)