How do you rationalize 2/(sqrt(72y))272y?

1 Answer
May 16, 2015

Let's remember that we use rationalization in order to remove roots from our denominator.

We proceed to do that by multiplying both numerator and denominator of your function by the same value as the root contained in the denominator. That way the proportion will be maintained and the root will be eliminated because

sqrt(f(x))sqrt(f(x))=f(x)f(x)f(x)=f(x)

That is because sqrtf(x)=f(x)^(1/2)f(x)=f(x)12, then f(x)^(1/2)f(x)^(1/2)=f(x)^(1/2+1/2)=f(x)^1=f(x)f(x)12f(x)12=f(x)12+12=f(x)1=f(x)

So, for your function:

2/(sqrt(72y))(sqrt(72y)/sqrt(72y)) = 2sqrt(72y)/(72y) = sqrt(72y)/(36y)272y(72y72y)=272y72y=72y36y

Your function has been rationalized, but we can further simplify it.

sqrt(72y)72y is the same as sqrt(2*36y)236y. We can take the root of 3636 out, like this: 6sqrt(2y)62y

Now, let's just simplify!

(6sqrt(2y))/(36y)=(sqrt(2y))/(6y)62y36y=2y6y