## Presentation on theme: "§ 7.4 Adding, Subtracting, and Dividing Radical Expressions."— Presentation transcript:

2 elephants + 3 elephants = 5 elephants
Combining Radicals Apples to apples, oranges to oranges,… you can only add “like” things…. Two or more radical expressions that have the same indices and the same radicands are called like radicals. Like radicals can be combined under addition in exactly the same way that we combined like terms under addition. Examples of this process follow. 2 elephants + 3 elephants = 5 elephants but 5 tigers + 3 gorillas = ??? Blitzer, Intermediate Algebra, 5e – Slide #2 Section 7.4

Combining Radicals EXAMPLE Simplify (add or subtract) by combining like radical terms: SOLUTION Apply the distributive property. Simplify. Group like terms. Apply the distributive property. Simplify. Blitzer, Intermediate Algebra, 5e – Slide #3 Section 7.4

Combining Radicals EXAMPLE Simplify by combining like radical terms, if possible: SOLUTION Factor the radicands using the greatest perfect square factors. Take the square root of each factor. Apply the distributive property. Blitzer, Intermediate Algebra, 5e – Slide #4 Section 7.4

CONTINUED Simplify. Factor the radicands using the greatest perfect cube factors. Take the cube root of each factor. Apply the distributive property. Simplify. Blitzer, Intermediate Algebra, 5e – Slide #5 Section 7.4

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. Blitzer, Intermediate Algebra, 5e – Slide #6 Section 7.4

Simplifying Radicals Simplify using the quotient rule: EXAMPLE
SOLUTION Blitzer, Intermediate Algebra, 5e – Slide #7 Section 7.4

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. Blitzer, Intermediate Algebra, 5e – Slide #8 Section 7.4

Combining Radicals Divide and, if possible, simplify:
EXAMPLE 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. Blitzer, Intermediate Algebra, 5e – Slide #9 Section 7.4

CONTINUED 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. Blitzer, Intermediate Algebra, 5e – Slide #10 Section 7.4