What Are Some Ways to Simplify Square Root Problems?

Simplifying square roots involves pulling as many integer factors outside the square root as possible. For example, the square root of 48, or sqrt(48), is equal to sqrt(16) * sqrt(3), which is 4 * sqrt(3). For a measurement, estimate sqrt(3) to 1.732, and multiply.

Removing perfect squares from an expression containing square roots is the most common way to simplify the expression. Combine multiple square root terms to one large term, then search for the largest factors of that term that are perfect squares. For example, combining the terms in the expression sqrt(2) * sqrt(3) * sqrt(48) into a single term yields sqrt(288). Its largest factor, 144, is a perfect square of 12. Moving 12 outside the square root creates 12 * sqrt(2).