Question

Rút gọn:  \(5\sqrt{x}+6\sqrt{\dfrac{x}{4}}-x\sqrt{\dfrac{4}{x}}+\sqrt{5}\) với x > 0

Answer 1

\(5\sqrt{x}+6\sqrt{\dfrac{x}{4}}-x\sqrt{\dfrac{4}{x}}+\sqrt{5}\) (x > 0)

\(=5\sqrt{x}+\dfrac{6}{2}\sqrt{x}-x\sqrt{\dfrac{4x}{x^2}}+\sqrt{5}\)

\(=5\sqrt{x}+3\sqrt{x}-2\sqrt{x}+\sqrt{5}\)

\(=6\sqrt{x}+\sqrt{5}\)

Answer 2

Lời giải:

\(5\sqrt{x}+6\sqrt{\frac{x}{4}}-x\sqrt{\frac{4}{x}}+\sqrt{5}=5\sqrt{x}+6.\sqrt{\frac{1}{4}}.\sqrt{x}-\sqrt{4}.\sqrt{x^2.\frac{1}{x}}+\sqrt{5}\)

\(=5\sqrt{x}+3\sqrt{x}-2\sqrt{x}+\sqrt{5}=6\sqrt{x}+\sqrt{5}\)