Question

Với A\(\ge\)0 , B>0

Chứng Minh: \(\sqrt{\dfrac{A}{B}}=\dfrac{1}{\left|B\right|}.\sqrt{AB}\)

Answer 1

Ta có :VP= \(\dfrac{1}{\left|B\right|}.\sqrt{A}.\sqrt{B}=\dfrac{\sqrt{A}.\sqrt{B}}{B}\)(vì B > 0)

\(=\dfrac{\sqrt{A}.\sqrt{B}}{\sqrt{B}.\sqrt{B}}=\dfrac{\sqrt{A}}{\sqrt{B}}=\sqrt{\dfrac{A}{B}}=VT\)(đpcm)

Answer 2

\(vp=\dfrac{1}{\left|B\right|}.\sqrt{AB}=\dfrac{\sqrt{A}.\sqrt{B}}{B}=\dfrac{\sqrt{A}}{\sqrt{B}}=\sqrt{\dfrac{A}{B}}=vt\)

Answer 3

Ta có :

\(\sqrt{\dfrac{A}{B}}=\dfrac{\sqrt{A}}{\sqrt{B}}=\dfrac{\sqrt{AB}}{\sqrt{BB}}=\dfrac{\sqrt{AB}}{\left|B\right|}=\dfrac{1}{\left|B\right|}\times\sqrt{AB}\) ( Vì B >0 )