Simplifying, Adding, and Subtracting Radicals

A radical is a symbol used to represent the root of a number, most commonly the square root. For example, √x represents the square root of x.

To simplify a radical expression, factor the number under the radical into its prime factors, and then extract any perfect squares (or higher powers) from under the radical.

The square root of 18 simplifies to 3√2.

To add radical expressions, combine like terms. This means you can only add radicals that have the same index and radicand.

The result of √18 - √12 is 3√2 - 2√3.

To subtract radical expressions, like terms are combined, similar to adding. Ensure the radicals have the same index and radicand.

The simplified form of 5√80 is 20√5.

The result is √7.

To simplify √150, factor it into √(25 * 6), which simplifies to 5√6.

The simplified form of 2√24 is 4√6.