Educator

Simplifying Radical Expressions

• A radical expression contains a square root. The expression inside the square root is called a radicand.

• To simplify a radical expression, extract all perfect squares from the radicand.

• Use the product and quotient properties of square roots to help you simplify radical expressions.

• If the exponent of the variable inside the radical is even and the resulting simplified expression has an odd exponent, take the absolute value of the expression for the simplified expression to guarantee that it is nonnegative.

• In simplified form, there can be no radicals in the denominator. Removing such radicals is called rationalizing the denominator.

• To rationalize a monomial denominator, simply multiply the numerator and denominator by the radical in the denominator.

• To rationalize a binomial denominator, multiply the numerator and denominator by the conjugate of the denominator. The conjugate is the same as the original binomial but with the sign between the first term and the second term reversed.

• To be in simplified form, there must be no perfect squares or fractions in the radicand and there must be no radicals in the denominator.