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Splash Screen. Learning Target. I CAN solve radical equations. Then/Now. Radical Equations – equations that contain radicals in the radicand. Concept.

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  1. Splash Screen

  2. Learning Target • I CAN solve radical equations. Then/Now

  3. Radical Equations – equations that contain radicals in the radicand. Concept

  4. FREE-FALL HEIGHT An object is dropped from an unknown height and reaches the ground in 5 seconds. Use the equation , where t is time in seconds and h isheight in feet, to find the heightfrom which the object was dropped. Variable as a Radicand Understand You know the time it takes for the object to hit the ground. You need to find the height. Example 1

  5. Variable as a Radicand Plan Solve Original equation Replace t with 5. Multiply each side by 4. Example 1

  6. ? ? Variable as a Radicand Square each side. 400 = h Simplify. Answer: The object was dropped from a height of 400 feet. Check by substituting 400 for h in the original equation. Original equation t = 5 and h = 400 5 = 5  Divide. Example 1

  7. A B C D A. 28 ft B. 11 ft C. 49 ft D. 784 ft Example 1

  8. Expression as a Radicand Original equation Subtract 8 from each side. Square each side. x = 52 Add 3 to each side. Answer: The solution is 52. Example 2

  9. A B C D A. 64 B. 60 C. 4 D. 196 Example 2

  10. Extraneous Solutions – when squaring each side of an equation you sometimes end up with a solution that is not a solution to the original equation.

  11. Check your solution. Variable on Each Side Original equation Square each side. 2 – y = y2 Simplify. 0 = y2+ y– 2 Subtract 2 and add y to each side. 0 = (y + 2)(y – 1) Factor. y + 2 = 0 or y – 1 = 0 Zero Product Property y = –2 y = 1 Solve. Example 3

  12. ? ? ? ? X  Variable on Each Side Check Answer: Since –2 does not satisfy the original equation, 1 is the only solution. Example 3

  13. A B C D A. 3 B. –1 C. –1, 3 D. –3 Example 3

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