10-1A Simplifying Radicals Algebra 1 Glencoe McGraw-HillLinda Stamper

You have simplified fractions. answer

Simplifying Radicals The simplest form of a radical expression is an expression that has: No perfect square factors other than 1 in the radicand. not simplified No fractions in the radicand. not simplified No radicals in the denominator of a fraction. not simplified Use the properties of radicals to simplify radical expressions. All radical answers must be in simplified form!

Product Property of Radicals Rewrite using a perfect square factor. An efficient method is to find the largest perfect square factor. Write each factor as a radical. Simplify.

Example 1Example 2Example 3 Example 4Example 5Example 6

Simplify. Why isn’t the answer Because the problem was not Example 1Example 2Example 3

Simplify. Example 4Example 5Example 6

Product Property of Radicals Rewrite using a perfect square factor. Write each factor as a radical. Simplify. Multiply radicals using the product property. Rewrite as one radical. Simplify.

Example 7Example 8Example 9

Simplify a square root with variables. When finding the principal square root of an expression containing variables, be sure that the result is not negative. It may seem that the answer is… What if x has a value of -2. Substitute -2 for x in the equation. ? even odd For radical expressions where the exponent of the variable inside the radical is even and the resulting simplified exponent is odd, you must use absolute value to ensure nonnegative results. ?

Simplify. Write the radicand as prime factors. Write the problem. Simplify. Use good form – alphabetical order (inside and outside of the radical) with radical last. If the power of the variable is an odd number, write the variable with absolute value bars

Simplify. You can have more than one variable in absolute value bars.

Simplify. Example 10 Example 11Example 12

Simplify. Example 10 Example 11Example 12

10-A2 Pages #17–28,68-70.