10-1A Simplifying Radicals Algebra 1 Glencoe McGraw-Hill Linda Stamper

You have simplified fractions. answer

All radical answers must be in simplified form! 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 All radical answers must be in simplified form! Use the properties of radicals to simplify radical expressions.

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

Simplify. Example 1 Example 2 Example 3 Example 4 Example 5 Example 6

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

Simplify. Example 4 Example 5 Example 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.

Simplify. Example 7 Example 8 Example 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. 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.

Write the radicand as prime factors. Simplify. Write the problem. Write the radicand as prime factors. 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 11 Example 12

Simplify. Example 10 Example 11 Example 12

Homework 10-A2 Pages 532-534 #17–28,68-70.