Question

Bài 1: rút gọn biểu thức

d)\(\sqrt{23+8\sqrt{7}}-\sqrt{7}\)

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

b)\(\sqrt{6-4\sqrt{2}}+\sqrt{2}\)

c)\(\sqrt{23+8\sqrt{7}}-\sqrt{7}\)

Answer 1

1)d) \(\sqrt{23+8\sqrt{7}}-\sqrt{7}\)

\(=\sqrt{4^2+2.4.\sqrt{7}+\sqrt{7^2}}-\sqrt{7}\)

\(=\sqrt{\left(4+\sqrt{7}\right)^2}-\sqrt{7}\)

\(=4+\sqrt{7}-\sqrt{7}\)

\(=4\)

Answer 2

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

=\(\sqrt{\left(\sqrt{2}\right)^2-2.2\sqrt{5}+\left(\sqrt{5}\right)^2}+\sqrt{5}\)

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

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

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

=\(\sqrt{2}\)