Rationalizing the DenominatorA series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.
Rationalizing the Denominator with Higher Roots When a denominator has a higher root, multiplying by the radicand will not remove the root. Instead, to rationalize the denominator we multiply by a number that will yield a new term that can come out of the root. For example, with a cube root multiply by a number that will give a cubic number such as 8, 27, or 64.
Rationalizing a Denominator with a Binomial When rationalizing a denominator with two terms, called a binomial, first identify the conjugate of the binomial. The conjugate is the same binomial except the second term has an opposite sign. Next, multiply the numerator and denominator by the conjugate. The denominator becomes a difference of squares, which will eliminate the square roots in the denominator.
Solving an Equation with Radicals Solving equations with radicals, no matter what power, involves isolating the radical on one side of the equation and then raising both sides of the equation to the power of the radical. When solving radicals, the final step is to isolate the variable. If there are more than one radical, we isolate and remove one root, then isolate and remove the other root. finally, we solve the remaining equation for the variable.
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