By OpenStax

Algebra and Trigonometry offers a entire and multi-layered exploration of algebraic rules. The textual content is appropriate for a regular introductory Algebra & Trigonometry path, and was once built for use flexibly. The modular strategy and the richness of content material guarantees that the e-book meets the desires of numerous courses. Algebra and Trigonometry courses and helps scholars with differing degrees of training and event with arithmetic. principles are offered as in actual fact as attainable, and development to extra complicated understandings with huge reinforcement alongside the best way. A wealth of examples - often a number of dozen consistent with bankruptcy - provide exact, conceptual motives, which will construct in scholars a powerful, cumulative beginning within the fabric sooner than asking them to use what they have realized. it is a full-color textbook.

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**Example text**

Simplify. Example 2 Using the Product Rule to Simplify Square Roots Simplify the radical expression. — — a. √ 162a5b4 Solution — a. √ 100 ∙ 3 — — 100 ∙ √ 3 √ — Factor perfect square from radicand. Write radical expression as product of radical expressions. 10√ 3 Simplify. 3 Radicals and Rational Expressions — b. √81a4b4 ∙ 2a — — √81a b ∙√ 2a 4 4 Factor perfect square from radicand. Write radical expression as product of radical expressions. — 9a b √2a Simplify. How To… Given the product of multiple radical expressions, use the product rule to combine them into one radical expression.

3 Radicals and Rational Expressions Solution Rewrite each term so they have equal radicands. — — — — — — — 2 — = 20√9 √ 4 √ 2 √ a √ a2 √ ( b2) √ c 20 √ 72a3b4c — = 20(3)(2)∣ a ∣b2√2ac = 120∣ a ∣b2√2ac — — — — — — — 2 — = 14√2 √4 √a √a2 √ ( b2) 14√8a3b4c √ c — = 14(2)∣ a ∣b2√2ac = 28∣ a ∣b2√2ac — Now the terms have the same radicand so we can subtract. — — — − 28∣ a ∣b2√2ac = 92∣ a ∣b2√2ac 120∣ a ∣b2√2ac Try It #7 — — Subtract 3√80x − 4√45x .

To do this, we use the power rule of exponents. Consider the expression (x 2)3. The expression inside the parentheses is multiplied twice because it has an exponent of 2. Then the result is multiplied three times because the entire expression has an exponent of 3. 3 factors (x 2)3 = (x 2) · (x 2) · (x 2) 2 factors 3 factors 2 factors 2 factors = x · x · x · x · x · x =x·x·x·x·x·x = x 6 The exponent of the answer is the product of the exponents: (x 2)3 = x 2 ∙ 3 = x 6.