Radicals and rational expressions
Pull the largest perfect square out of a radical, and cancel only whole factors in a rational expression.
A worked example
√48 = √16 x √3 = 4√3. And (x^2 - 49) / (x + 7) factors to (x - 7)(x + 7) / (x + 7) = x - 7, provided x ≠ -7.
The mistake people actually make
Cancel factors, never single terms. State the non-permissible values from the original denominator, before any cancelling hides them.