Question

Rút gọn:
\(\sqrt{x+2\sqrt{x-1}}\)

Answer 1

\(\sqrt{x+2\sqrt{x-1}}\)(ĐK:x\(\ge1\))

\(=\sqrt{\left(x-1\right)+2\sqrt{x-1}+1}\)

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

\(=\left|\sqrt{x-1}+1\right|\)

\(=\sqrt{x-1}+1\)

Answer 2

\(\sqrt{x+2\sqrt{x-1}}\)

\(=\sqrt{x-1+2\sqrt{x-1}+1}\)

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

\(=\left|\sqrt{x-1}+1\right|\)

\(=\sqrt{x-1}+1\)

\(\)

Answer 3

ĐKXĐ \(x\ge 1\)

\(\sqrt{x+2\sqrt{x-1} } \)\(=\sqrt{x-1+2\sqrt{x-1}+1 } =\sqrt{(\sqrt{x-1}+1)^2 } =|\sqrt{x-1}+1| =\sqrt{x-1}+1 \)