1. § 7.4 Adding, Subtracting, and Dividing Radical Expressions

2. Blitzer, Intermediate Algebra, 4e – Slide #53 Combining RadicalsEXAMPLE Simplify (add or subtract) by combining like radical terms: SOLUTION Apply the distributive property. Simplify. Apply the distributive property. Group like terms. Simplify.

3. Blitzer, Intermediate Algebra, 4e – Slide #54 Combining RadicalsEXAMPLE Simplify by combining like radical terms, if possible: SOLUTION Factor the radicands using the greatest perfect square factors. Apply the distributive property. Take the square root of each factor.

4. Blitzer, Intermediate Algebra, 4e – Slide #55 Combining Radicals Factor the radicands using the greatest perfect cube factors. Simplify. Take the cube root of each factor. CONTINUED Apply the distributive property. Simplify.

5. Blitzer, Intermediate Algebra, 4e – Slide #56 Simplifying Radicals The Quotient Rule for Radicals If and are real numbers and, then The nth root of a quotient is the quotient of the nth roots.

6. Blitzer, Intermediate Algebra, 4e – Slide #57 Simplifying RadicalsEXAMPLE Simplify using the quotient rule: SOLUTION

7. Blitzer, Intermediate Algebra, 4e – Slide #58 Combining Radicals Dividing Radical Expressions If and are real numbers and, then To divide two radical expressions with the same index, divide the radicands and retain the common index.

8. Blitzer, Intermediate Algebra, 4e – Slide #59 Combining RadicalsEXAMPLE Divide and, if possible, simplify: SOLUTION In each part of this problem, the indices in the numerator and the denominator are the same. Perform each division by dividing the radicands and retaining the common index. Divide the radicands and retain the common index. Divide factors in the radicand. Subtract exponents on common bases.

9. Blitzer, Intermediate Algebra, 4e – Slide #60 Combining RadicalsCONTINUED Simplify. Factor using the greatest perfect square factor. Factor into two radicals. Simplify. Divide the radicands and retain the common index. Divide factors in the radicand. Subtract exponents on common bases.

10. Blitzer, Intermediate Algebra, 4e – Slide #61 Combining RadicalsCONTINUED Simplify. Factor using the greatest perfect square factor. Factor into two radicals. Simplify.