Rewrite the square roots as one-half exponents. Taking the square root of a term is the same as that same term to the one-half power.
Combine the top and the bottom of the fraction under the same one-half exponent as a potential next step. It is possible that the integral can be then solved using the power rule. However, it is also possible that this will just complicate the situation more and should be avoided.
Substitute for all or part of the terms underneath the square root symbol. This works best when there is a polynomial, such as a quadratic, underneath the square root. Remember to replace the differential term with the derivative of the substitution variable.
Use a trigonometric substitution. If neither of the previous two strategies convert the integrand into a form that can be easily integrated, set various trigonometric functions equal to all or part of the term under the square root and substitute. See the Resource section for a table of integrals.