That choice is made so that after they are multiplied, everything under the radical sign will be perfect cubes. What can be multiplied with so the result will not involve a radical? The answer is or. Note we elected to find 's principal root. To rationalize this denominator, the appropriate fraction with the value 1 is, since that will eliminate the radical in the denominator, when used as follows:

This is accomplished by multiplying the expression by a fraction having the value 1, in an appropriate form. This process is called rationalizing the denominator. The radicand contains no factor (other than 1) which is the nth or greater power of an integer or polynomial.Īn expression with a radical in its denominator should be simplified into one without a radical in its denominator. Radical expressions are written in simplest terms when That's a mathematical symbols way of saying that when the index is even there can be no negative number in the radicand, but when the index is odd, there can be. When dividing radical expressions, use the quotient rule.

Quiz: Binomial Coefficients and the Binomial Theorem.

Binomial Coefficients and the Binomial Theorem.

Quiz: Definition and Examples of Sequences.

Quiz: Exponential and Logarithmic Equations.

Systems of Equations Solved Algebraically.

Systems of Inequalities Solved Graphically.

Quiz: Systems of Equations Solved Graphically.

Systems of Equations Solved Graphically.

Quiz: Systems of Equations Solved Algebraically.

Quiz: Solving Equations in Quadratic Form.

Quiz: Solving Quadratics by the Quadratic Formula.

Solving Quadratics by the Quadratic Formula.

Quiz: Solving Quadratics by Completing the Square.

Solving Quadratics by Completing the Square.

Quiz: Solving Quadratics by the Square Root Property.

Solving Quadratics by the Square Root Property.

Quiz: Adding and Subtracting Radical Expressions.

Adding and Subtracting Radical Expressions.

Quiz: Proportion, Direct Variation, Inverse Variation, Joint Variation.

Proportion, Direct Variation, Inverse Variation, Joint Variation.

Quiz: Adding and Subtracting Rational Expressions.

Adding and Subtracting Rational Expressions.

Quiz: Trinomials of the Form ax^2 + bx + c.

Quiz: Trinomials of the Form x^2 + bx + c.

Quiz: Adding and Subtracting Polynomials.

Quiz: Linear Equations: Solutions Using Elimination with Three Variables.

Linear Equations: Solutions Using Elimination with Three Variables.

Quiz: Linear Equations: Solutions Using Determinants with Three Variables.

Linear Equations: Solutions Using Determinants with Three Variables.

Quiz: Linear Equations: Solutions Using Matrices with Three Variables.

Linear Equations: Solutions Using Matrices with Three Variables.

Quiz: Linear Inequalities: Solutions Using Graphing with Two Variables.

Linear Inequalities: Solutions Using Graphing with Two Variables.

Quiz: Linear Equations: Solutions Using Determinants with Two Variables.

Linear Equations: Solutions Using Determinants with Two Variables.

Quiz: Linear Equations: Solutions Using Matrices with Two Variables.

Quiz: Linear Equations: Solutions Using Graphing with Two Variables.

Linear Equations: Solutions Using Graphing with Two Variables.

Linear Equations: Solutions Using Matrices with Two Variables.

Quiz: Linear Equations: Solutions Using Elimination with Two Variables.

Linear Equations: Solutions Using Elimination with Two Variables.Quiz: Linear Equations: Solutions Using Substitution with Two Variables.

Linear Equations: Solutions Using Substitution with Two Variables.Quiz: Slopes of Parallel and Perpendicular Lines.Slopes of Parallel and Perpendicular Lines.

Simplify radical expressions