Simplifying Radical Expressions
When simplifying a radical expression, find the factors that are to the nth powers of the radicand and then use the Product Property of Radicals. What is the Product Property of Radicals???
For any real numbers a and b, and any integer n, n>1, 1. If n is even, then When a and b are both nonnegative. 2. If n is odd, then Product Property of Radicals
Let’s do a few problems together. Factor into squares Product Property of Radicals
Product Property of Radicals Factor into cubes if possible Product Property of Radicals
For real numbers a and b, b 0, And any integer n, n>1, Quotient Property of Radicals Ex:
The radicand contains no fractions. No radicals appear in the denominator.(Rationalization) The radicand contains no factors that are nth powers of an integer or polynomial. In general, a radical expression is simplified when:
Simplify each expression. Rationalize the denominator Answer
To simplify a radical by adding or subtracting you must have like terms. Like terms are when the powers AND radicand are the same.
Here is an example that we will do together. Rewrite using factors Combine like terms
You can add or subtract radicals like monomials. You can also simplify radicals by using the FOIL method of multiplying binomials. Let us try one.
When there is a binomial with a radical in the denominator of a fraction, you find the conjugate and multiply. This gives a rational denominator.
Simplify: Multiply by the conjugate. FOIL numerator and denominator. Next
Combine like terms Try this on your own: