A ajorden New member Joined Mar 13, 2012 Messages 8 Mar 26, 2012 #1 How do I rationalize the denominator ? 5x / √3x4y I think I begin by multiplying both the numerator and denominator by √3x4y So then I have 5x√3x4y / 3x4y Now I'm not sure what to do after this? Thanks
How do I rationalize the denominator ? 5x / √3x4y I think I begin by multiplying both the numerator and denominator by √3x4y So then I have 5x√3x4y / 3x4y Now I'm not sure what to do after this? Thanks
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 Mar 26, 2012 #2 Hello, ajorden! Another approach . . . \(\displaystyle \text{How do I rationalize the denominator? }\:\dfrac{5x}{\sqrt{3x^4y}}\) Click to expand... Simplify the denominator first: . . \(\displaystyle \sqrt{3x^4y} \:=\:\sqrt{x^4\cdot 3y} \:=\:\sqrt{x^4}\sqrt{3y} \:=\:x^2\sqrt{3y}\) The problem becomes: .\(\displaystyle \dfrac{5x}{x^2\sqrt{3y}} \:=\:\dfrac{5}{x\sqrt{3y}}\) Multiply by \(\displaystyle \dfrac{\sqrt{3y}}{\sqrt{3y}}\!:\;\;\dfrac{5}{x\sqrt{3y}}\cdot\dfrac{\sqrt{3y}}{\sqrt{3y}} \;=\;\dfrac{5\sqrt{3y}}{x\cdot3y} \;=\;\dfrac{5\sqrt{3y}}{3xy} \)
Hello, ajorden! Another approach . . . \(\displaystyle \text{How do I rationalize the denominator? }\:\dfrac{5x}{\sqrt{3x^4y}}\) Click to expand... Simplify the denominator first: . . \(\displaystyle \sqrt{3x^4y} \:=\:\sqrt{x^4\cdot 3y} \:=\:\sqrt{x^4}\sqrt{3y} \:=\:x^2\sqrt{3y}\) The problem becomes: .\(\displaystyle \dfrac{5x}{x^2\sqrt{3y}} \:=\:\dfrac{5}{x\sqrt{3y}}\) Multiply by \(\displaystyle \dfrac{\sqrt{3y}}{\sqrt{3y}}\!:\;\;\dfrac{5}{x\sqrt{3y}}\cdot\dfrac{\sqrt{3y}}{\sqrt{3y}} \;=\;\dfrac{5\sqrt{3y}}{x\cdot3y} \;=\;\dfrac{5\sqrt{3y}}{3xy} \)
