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4.5 Solve Quadratic Equations by Finding Square Roots

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EXAMPLE 1 Use properties of square roots Simplify the expression. 5= 4a. 80 5 16 = = 3 14b. 6 21 126 = 9 14 = c. 4 81 = 4 = 2929 d. 7 16 = 7 = 4 7

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

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GUIDED PRACTICE for Example 1 3. 6 510 15 4. 8 2814 4 ANSWER

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GUIDED PRACTICE for Example 1 5. 3838 9 64 6. 15 4 2 ANSWER

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GUIDED PRACTICE for Example 1 7. 11 25 8. 36 49 5 11 7 6 ANSWER

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

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EXAMPLE 2 Rationalize denominators of fractions. SOLUTION (b) 3 7 + 2 = 3 2 7 – 2 2 = 21 – 3 2 49 – 7 + 7 – 2 22 = 21 – 32 47

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EXAMPLE 3 Solve a quadratic equation Solve 3x 2 + 5 = 41. 3x 2 + 5 = 41 Write original equation. 3x 2 = 36 Subtract 5 from each side. x 2 = 12 Divide each side by 3. x = + 12 Take square roots of each side. x = + 43 + 2 3 Product property Simplify.

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

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EXAMPLE 4 Standardized Test Practice SOLUTION 1515 (z + 3) 2 = 7 Write original equation. (z + 3) 2 = 35 Multiply each side by 5. z + 3 = + 35 Take square roots of each side. z = –3 + 35 Subtract 3 from each side. The solutions are –3 + and –3 – 35

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

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GUIDED PRACTICE for Examples 2, 3, and 4 GUIDED PRACTICE Simplify the expression. 9. 5 30 6 5 10. 9 8 2 4 3 11. 17 12 51 6 ANSWER 12. 399 21 19 21 – 21 – 35 22 13. – 6 7 – 5 8 – 211 5 14. 2 4 + 11 ANSWER

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– 9 +7 74 for Examples 2, 3, and 4 GUIDED PRACTICE 15. – 1 9 + 7 32 + 4 3 61 16. 4 8 – 3 ANSWER

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for Examples 2, 3, and 4 GUIDED PRACTICE 17. Solve the equation. 5x 2 = 80 + 4 18. z 2 – 7 = 29 + 6 19. 3(x – 2) 2 = 40 120 3 2 + ANSWER

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