Exponents and Radicals

[ajorden]

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

 

[soroban]

Hello, ajorden!

Another approach . . .

\(\displaystyle \text{How do I rationalize the denominator? }\:\dfrac{5x}{\sqrt{3x^4y}}\)

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 \(\displaystyle \dfrac{\sqrt{3y}}{\sqrt{3y}}\!:\;\;\dfrac{5}{x\sqrt{3y}}\cdot\dfrac{\sqrt{3y}}{\sqrt{3y}} \;=\;\dfrac{5\sqrt{3y}}{x\cdot3y} \;=\;\dfrac{5\sqrt{3y}}{3xy} \)