Question

Rút gọn biểu thức : \(\sqrt{\dfrac{b}{a}}+\sqrt{ab}+\dfrac{b}{a}\sqrt{\dfrac{a}{b}}\)

Answer 1

\(\sqrt{\dfrac{b}{a}}+\sqrt{ab}+\dfrac{b}{a}\sqrt{\dfrac{a}{b}}\)

\(=\dfrac{\sqrt{b}}{\sqrt{a}}+\sqrt{a}.\sqrt{b}+\dfrac{b}{a}.\dfrac{\sqrt{a}}{\sqrt{b}}\)

\(=\sqrt{b}.\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)+\dfrac{\sqrt{b}}{\sqrt{a}}\)

\(=\sqrt{b}.\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}+\dfrac{1}{\sqrt{a}}\right)\)

\(=\sqrt{b}.\left(\dfrac{1+a+1}{\sqrt{a}}\right)\)

\(=\dfrac{\sqrt{b}.\left(a+2\right)}{\sqrt{a}}=\dfrac{\sqrt{ab}+2\sqrt{b}}{\sqrt{a}}\)

Chúc bạn học tốt!!!