Question

Rút gọn các biểu thức

A= \(\sqrt{\left(\sqrt{2}-1\right)^2}\)-\(\sqrt{3+2\sqrt{2}}\)

B= \(\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)

C= \(\sqrt{\left(2\sqrt{5}-7\right)^2}\)-\(\sqrt{45-20\sqrt{5}}\)

D= \(\sqrt{\left(3-\sqrt{5}\right)^2}\)+\(\sqrt{5}\)

Answer 1

\(A=\sqrt{\left(\sqrt{2}-1\right)^2}-\sqrt{3+2\sqrt{2}}\)

\(A=\sqrt{2}-1-\sqrt{\left(\sqrt{2}+1\right)^2}\)

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

B = \(\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)

\(B=\sqrt{6+2\sqrt{5}-\sqrt{29-6\sqrt{20}}}\)

B = \(\sqrt{6+2\sqrt{5}-\sqrt{\left(3-\sqrt{20}\right)^2}}\)

\(B=\sqrt{6+2\sqrt{5}-2\sqrt{5}+3}\)

\(B=\sqrt{9}=3\)