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Simplify Radical Expressions

Simplify Radical Expressions. What steps would you take in simplifying the following: √(3+9 2 ). EQs…. How do we simplify algebraic and numeric expressions involving square root? How do we perform operations with square roots?. Vocabulary.

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Simplify Radical Expressions

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  1. Simplify Radical Expressions What steps would you take in simplifying the following: √(3+92)

  2. EQs… • How do we simplify algebraic and numeric expressions involving square root? • How do we perform operations with square roots?

  3. Vocabulary • Simplest Form – A radical expression is in simplest form if no perfect square factors other than 1 are in the radicand, no fractions are in the radicand, and no radicals appear in the denominator of the fraction. • Rationalizing the Denominator – The process of eliminating a radical from an expression’s denominator.

  4. Vocabulary • Radical Conjugates – • Product Property of Radicals – States that the square root of a product equals the product of the square roots of the factors. • Quotient Property of Radicals – States that the square roots of a quotient equals the quotient of the square roots of the numerator and denominator.

  5. Example 1Use the product property of radicals • Simplify the expression.

  6. Multiplying Radicals * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

  7. Multiply and then simplify

  8. Example 2Multiply radicals • Simplify the expression.

  9. Example 3Use the quotient property of radicals • Simplify the expression.

  10. Guided Practice for Examples 1, 2, & 3 • Simplify the expression.

  11. Guided Practice for Examples 1, 2, & 3 • Simplify the expression.

  12. Example 4Rationalize the denominator

  13. Combining Radicals + To combine radicals: combine the coefficients of like radicals

  14. Simplify eachexpression

  15. Simplify each expression: Simplify each radical first and then combine.

  16. Example 5Add and Subtract Radicals

  17. Guided Practice for Examples 4 & 5Add and Subtract Radicals

  18. Joke of the Day… • Why was the math book crying?

  19. It had too many problems!

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