Lesson 5

Lesson 5 Summary

The key to rationalizing a denominator is to create an equivalent fraction that does not have a radical in the denominator. You learned very early in your math education that you could multiply any number or expression by 1 and get the same expression. Any fraction that has exactly the same value in both the numerator and the denominator is equal to 1. Therefore, to eliminate a radical in the denominator, you multiply both the numerator and the denominator by the radical, which is simply multiplying by 1. The final step is always to put the expression in its simplest terms.

When solving equations involving radicals, there are times when a negative answer is the only possible solution; but when you see a square root sign, you are only asked to give the principal (positive) square root of the radicand. If you are required to give a secondary (negative) square root, it will be indicated by a negative sign in front of the radical sign. If you are required to give both the principal and secondary square roots of a radicand, it will be indicated by a plus or minus symbol in front of the radical sign.

In the next lesson you will apply the skills you have been developing in this module to solve problems involving radical equations.