Rationalizing Denominators Containing Radicals

Rationalizing a denominator means rewriting a fraction so that no radical remains in the denominator.

During an algebra class, Professor Carter challenges his students to rewrite one divided by the cube root of two with a rational denominator.

Because the cube root of two is irrational, its decimal representation does not terminate or repeat. Instead of using a decimal approximation, the students use an algebraic method.

Maya, one of the students, realizes that an algebraic trick can simplify the calculation. To eliminate the irrational denominator, she needs to create a perfect cube.

Since two times four is eight, a perfect cube, she multiplies the fraction by the cube root of four over itself. Because this factor equals one, the value remains unchanged.

The denominator becomes the cube root of eight, which simplifies to two. This leaves the cube root of four divided by two, with no radical in the denominator.

Professor Carter reminds the class that rationalizing a denominator involves multiplying the numerator and denominator by the same factor to eliminate the radical from the denominator without changing the expression's value.