Question

Rút gọn các biểu thức:

\(a,\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)

\(b,\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)

Answer 1

a, \(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)

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

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

\(=\left|1+\sqrt{5}\right|+\left|\sqrt{5}-1\right|\)

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

b, \(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)

\(=\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{1}+1}\)

\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)}\)

\(=\left|\sqrt{7}-1\right|-\left|\sqrt{7}+1\right|\)

\(=\sqrt{7}-1-\sqrt{7}-1=-2\)