In my calculus class a few days ago, my professor was going over how to find three dimensional velocity and its magnitude. In the problem, the magnitude of the velocity came out to be $\displaystyle \sqrt{9+36t^2+36t^4}=3+6t^2$.

My question is, how did he simplify the equation under the square root so that it became $\displaystyle 3+6t^2$?

For the homework, I need to simplify these two square root equations to get something without a square root sign (if possible). Can you guys help me out with this? Thanks.

1) $\displaystyle \sqrt{9t^4+36+36t^2}$

2) $\displaystyle \sqrt{(-3cost)^2+(-4cost)^2+(-5sint)^2)}$