Question

Bài 3 Rút gọn

Answer 1

a) Ta có: \(\sqrt{12-2\sqrt{11}}\)

\(=\sqrt{11-2\cdot\sqrt{11}\cdot1+1}\)

\(=\sqrt{11}-1\)

b) Ta có: \(\sqrt{24+8\sqrt{5}}\)

\(=\sqrt{20+2\cdot2\sqrt{5}\cdot2+4}\)

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

c) Ta có: \(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}\)

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

=1

d) Ta có: \(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)

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

\(=2\sqrt{3}\)

e) Ta có: \(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)

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

\(=2\sqrt{2}\)

f) Ta có: \(\sqrt{17-12\sqrt{2}}-\sqrt{9+4\sqrt{2}}\)

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

\(=2-4\sqrt{2}\)