Question

Rút gọn căn thức sau:

\(\sqrt{17+12\sqrt{2}}\) +\(\sqrt{9+4\sqrt{2}}\)

Answer 1

\(\sqrt{17+12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)

\(=\sqrt{\left(3+2\sqrt{2}\right)^2}+\sqrt{\left(2\sqrt{2}+1\right)^2}\)

\(=3+2\sqrt{2}+2\sqrt{2}+1\)

\(=4+4\sqrt{2}\)

Answer 2

\(\sqrt{17+12\sqrt{2}}+\sqrt{9+4\sqrt{2}}=\sqrt{\left(3+2\sqrt{2}\right)^2}+\sqrt{\left(2\sqrt{2}+1\right)^2}\)

\(=3+2\sqrt{2}+2\sqrt{2}+1=4+4\sqrt{2}\)

Answer 3

\(\sqrt{17+12\sqrt{2}}+\sqrt{9+4\sqrt{2}}=\sqrt{8+2.2\sqrt{2}.3+9}+\sqrt{8+2.2\sqrt{2}.1+1}=\sqrt{\left(2\sqrt{2}+3\right)^2}+\sqrt{\left(2\sqrt{2}+1\right)^2}=\left|2\sqrt{2}+3\right|+\left|2\sqrt{2}+1\right|=2\sqrt{2}+3+2\sqrt{2}+1=4\sqrt{2}+4\)