Question

rút gọn biểu thức:

  M=Căn(4+căn7)-căn(4-căn7)

Answer 1

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

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

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

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

\(M^2=8-2\sqrt{16-7}\)

\(M^2=8-2\sqrt{9}=8-2.3=8-6=2\)

\(M=\frac{+}{ }\sqrt{2}\)