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Chapter 4.5 Solve Quadratic Equations by Finding Square Roots

Chapter 4.5 Solve Quadratic Equations by Finding Square Roots. = 4. =. a. =. =. b. = 3. 7. 5. 9. 4. 6. 5. 7. 7 . 4. 2 9. 4. 16. 80. 14. 81. 14. 16. 21. =. c. 81. 16. =. 126. =. d. =. EXAMPLE 1. Use properties of square roots. Simplify the expression.

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Chapter 4.5 Solve Quadratic Equations by Finding Square Roots

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  1. Chapter 4.5 Solve Quadratic Equations by Finding Square Roots

  2. = 4 = a. = = b. = 3 7 5 9 4 6 5 7 7 4 2 9 4 16 80 14 81 14 16 21 = c. 81 16 = 126 = d. = EXAMPLE 1 Use properties of square roots Simplify the expression.

  3. 3 7 3 2 27 98 for Example 1 GUIDED PRACTICE GUIDED PRACTICE ANSWER ANSWER

  4. 10 8 5 6 14 15 28 4 for Example 1 GUIDED PRACTICE GUIDED PRACTICE ANSWER ANSWER

  5. 9 15 3 8 2 64 4 15 for Example 1 GUIDED PRACTICE GUIDED PRACTICE ANSWER ANSWER

  6. 11 36 11 5 25 49 6 7 for Example 1 GUIDED PRACTICE GUIDED PRACTICE ANSWER ANSWER

  7. 3 7 + 5 2 2 2 5 5 2 2 5 (a) = 2 2 = 10 2 = EXAMPLE 2 Rationalize denominators of fractions. Simplify and (a) (b) SOLUTION

  8. 3 3 7 + 7 + 7 – (b) = 7 – 2 2 2 2 2 2 2 2 21 – 3 = 49 – 7 + 7 – 2 21 – 3 = 47 EXAMPLE 2 Rationalize denominators of fractions. SOLUTION

  9. 3 3 4 + x = 12 + x = + 2 x = EXAMPLE 3 Solve a quadratic equation Solve 3x2 + 5 = 41. 3x2 + 5 = 41 Write original equation. 3x2 = 36 Subtract 5 from each side. x2 = 12 Divide each side by 3. Take square roots of each side. Product property Simplify.

  10. – 2 2 3 3 ? ? 3( )2 + 5 = 41 3( )2 + 5 = 41 2 – 2 3 3 ? ? 3(12) + 5 = 41 3(12) + 5 = 41 41 = 41 41 = 41   EXAMPLE 3 Solve a quadratic equation ANSWER The solutions are and Check the solutions by substituting them into the original equation. 3x2 + 5 = 41 3x2 + 5 = 41

  11. 35 35 35 35 (z + 3)2 = 7 15 z + 3 = + z = –3 + The solutions are –3 + and –3 – EXAMPLE 4 Standardized Test Practice SOLUTION Write original equation. (z + 3)2 = 35 Multiply each side by 5. Take square roots of each side. Subtract 3 from each side.

  12. EXAMPLE 4 Standardized Test Practice ANSWER The correct answer is C.

  13. 17 5 5 19 11 6 11 9 – 6 2 12 21 5 8 4 + 7 – 30 5 3 – 21 – 3 8 – 2 399 2 51 4 21 22 5 6 for Examples 2, 3, and 4 GUIDED PRACTICE GUIDED PRACTICE Simplify the expression. ANSWER ANSWER ANSWER ANSWER ANSWER ANSWER

  14. 7 7 3 3 – 1 4 9 + 8 – – 9 + 32 + 4 74 61 for Examples 2, 3, and 4 GUIDED PRACTICE ANSWER ANSWER

  15. 120 + 2 3 + 4 + 6 for Examples 2, 3, and 4 GUIDED PRACTICE Solve the equation. 5x2 = 80 ANSWER z2 – 7 = 29 ANSWER 3(x – 2)2 = 40 ANSWER

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