Question

Bài 3: rút gọn
a)\(\sqrt{\dfrac{2a}{3}}.\sqrt{\dfrac{3a}{8}}\) với a≥0
b)\(\dfrac{2a+\sqrt{ab}-3b}{2a-5\sqrt{ab}+3b}\) với a≥0; b≥0; a≠b

Answer 1

a) \(\sqrt{\dfrac{2a}{3}}.\sqrt{\dfrac{3a}{8}}=\sqrt{\dfrac{6a^2}{24}}=\sqrt{\dfrac{a^2}{4}}=\dfrac{\sqrt{a^2}}{\sqrt{2^2}}=\dfrac{a}{2}\)  ( vì \(a\ge0\) )

Answer 2

b: \(\dfrac{2a+\sqrt{ab}-3b}{2a-5\sqrt{ab}+3b}\)

\(=\dfrac{2a-2\sqrt{ab}+3\sqrt{ab}-3b}{2a-2\sqrt{ab}-3\sqrt{ab}+3b}\)

\(=\dfrac{2\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)+3\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}{2\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)-3\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}\)

\(=\dfrac{2\sqrt{a}+3\sqrt{b}}{2\sqrt{a}-3\sqrt{b}}\)