I would first start of by rewriting the integrand. Recall that

.

I will take the positive square root since surface area must be positive. Therefore, the integrand can be simplified to:

Thus the integral becomes:

Apply a substitution...primarily . Thus . Solving for , we get .

Before we substitute, we can change the limits of integration as well. The upper limit will become and the lower limit will become .

Now, the integral can be rewritten as:

evaluating the integral we get:

.

Hope that helped you out!