Question

Rút gọn biểu thức:

\(A=\sqrt{\left(\sqrt{7}-2\right)^2}+\sqrt{\left(\sqrt{7}-5\right)^2}\)

\(B=\sqrt{23+8\sqrt{7}}-\sqrt{7}\)

\(C=\sqrt{11+2\sqrt{30}}-\sqrt{11-2\sqrt{30}}\)

Answer 1

\(A=\sqrt{7}-2+\sqrt{7}-5\\ =2\sqrt{7}-7\\ =\sqrt{7}\left(2-\sqrt{7}\right)\)

Answer 2

\(B=\sqrt{16+8\sqrt{7}+7}-\sqrt{7}\)

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

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

Answer 3

\(C=\sqrt{6+2\sqrt{30}+5}-\sqrt{6-2\sqrt{30}+5}\\ =\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{6}-\sqrt{5}\right)^2}\\ =\sqrt{6}+\sqrt{5}-\sqrt{6}+\sqrt{5}\\ =2\sqrt{5}\)