We are about to consider expressions involving variables inside of square roots. In order to make the simplification rules simpler, and to avoid a discussion of the "domain" of the square root, we assume that all variables represent non-negative real numbers.
Simplifying square roots with variables is similar to simplifying square roots without variables. Treat the variable as a factor--if it appears twice ( x 2 ), cross out both and write the factor ( x ) one time to the left of the square root sign. If the factor appears three times ( x 3 ), treat this as x 2×x : cross out x 2 and write x to the left of the square root sign, leaving the single x inside the square root sign.
In general, follow these rules:
Example 1: Simplify
Example 2: Simplify