# Simplifying Square Roots

1. May 26, 2014

### mill

1. The problem statement, all variables and given/known data

Find the arclength of the parametrized path x(t) = (t^2)/2 , y(t) = (t^3)/3 for 1<t<3.

2. Relevant equations

Arc Length Formula

3. The attempt at a solution

x'=t and y'=t^2.

Putting them into the arc length formula, I get sqrt(t^2 + t^4) inside.

I'm confused about how to simplify this part. The answer (10sqrt(10)-2sqrt(2))/3 suggests the quadratic formula somewhere along the way. I could probably pull out a variable into sqrt(t^2(t^2 + 1)) or tsqrt(t^2+1) but how do I use the quadratic equation in this case?

2. May 26, 2014

### Dick

You don't use the quadratic equation. You just integrate $t \sqrt{t^2+1}$. It's not hard, just do it by a substitution.

3. May 26, 2014

Thanks.