Question

Rút gọn: a)\(\sqrt{14+6\sqrt{5}}\)

Answer 1

\(\sqrt{14+6\sqrt{5}}=\sqrt{9+2\cdot3\cdot\sqrt{5}+5}=\sqrt{\left(3+\sqrt{5}\right)^2}=3+\sqrt{5}\)

Answer 2

\(\sqrt{14+6\sqrt{5}}\)

\(=\sqrt{3^2+2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}\)

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

\(=\left|3+\sqrt{5}\right|\)

\(=3+\sqrt{5}\)

Answer 3

a,Ta có :\(\sqrt{14+6\sqrt{5}}=\sqrt{5+2.\sqrt{5}.3+9}=\sqrt{\left(\sqrt{5}+9\right)^2}=\sqrt{5}+9\)