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Understanding Radicals and Expressions in Algebra

This educational resource delves into key concepts related to radicals in algebra, such as identifying the radicand and working with square roots. It includes exercises for evaluating expressions, comparing graphs, and applying the distributive property for equivalent expressions. The content is structured with prerequisite skills to enhance comprehension, making it suitable for learners aiming to solidify their algebra foundation. Through practice problems, it encourages students to master factoring and understanding quadratic expressions.

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Understanding Radicals and Expressions in Algebra

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  1. The number or expression inside a radical symbol is called the ? . 1. ANSWER radicand If b2 =a, then bis a(n) ? of a. 2. ANSWER square root Prerequisite Skills VOCABULARY CHECK Copy and complete the statement.

  2. Graph y = 3 2x. Compare the graph with the graph of y = 2x. 3. ANSWER the graph is a vertical stretch of y= 2x. 4. 81 ANSWER 9 Prerequisite Skills SKILL CHECK Evaluate the expression.

  3. – 64 5. – 8 ANSWER 6. 100 + 10 – ANSWER 7. – 121 ANSWER – 11 + – Prerequisite Skills SKILL CHECK

  4. 8. 4(y – 3) 10. – x(x + 11) ANSWER 4y – 12 ANSWER – x2 – 11x 9. 2(x – 2) 11. 4x(x – 9) 2x – 4 ANSWER 4x2 – 36x ANSWER Prerequisite Skills SKILL CHECK Use the distributive property to write an equivalent expression.

  5. 12. x2 + 4x + 4 14. r2 +8r + 7 ANSWER (x + 2)2 ANSWER (r + 7)(r + 1) 13. m2 + 9m + 8 15. b2 + 10b + 16 (m + 8)(m + 1) ANSWER ANSWER 49 (b + 8)(b + 2) ANSWER 16. Evaluatea2whena = 7 Prerequisite Skills SKILL CHECK Factor the trinomial.

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