1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental Mathematics Section 14.2: Simplifying Radicals

2. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Algebraic Expressions with Square Roots Properties of Square Roots If a and b are positive real numbers, then Simplest Form for Square Roots A square root is considered to be in simplest form when the radicand has no perfect square as a factor.

3. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Numerical Expressions with Square Roots Simplify each numerical expression so that there are no perfect square factors in the radicand.

4. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Radical Expressions with Variables Square Root of x 2 If x is a real number, then Note: If x ≥ 0 is given, then we can write

5. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Square Roots with Variables Simplify each of the following radical expressions. Assume that all variables represent positive real numbers. (Note that, by making this assumption, we need not be concerned about the absolute value sign.)

6. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Square Roots with Variables

7. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Square Roots Simplify each of the following radical expressions. Look for perfect square factors and even powers of the variables. Assume that all variables represent positive real numbers.

8. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Square Roots

9. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Algebraic Expressions with Cube Roots Simplest Form for Cube Roots A cube root is considered to be in simplest form when the radicand has no perfect cube as a factor.

10. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Expressions with Cube Roots CC