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Solving Radical Equations: Techniques and Examples

This lesson covers the fundamentals of solving radical equations, which contain variables within a square root or other root. We will explore various examples, including equations with a variable on each side and expressions inside the radicals. Key steps include isolating the radical, squaring both sides to eliminate the radical, simplifying, and verifying solutions. We will also apply these concepts to real-life scenarios, such as determining the height from which an object is dropped based on its free-fall time.

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Solving Radical Equations: Techniques and Examples

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  1. Example 1Radical Equation with a Variable Example 2Radical Equation with an Expression Example 3Variable on Each Side Lesson 3 Contents

  2. Use the equation to replace t with 5 seconds. Original equation Replace t with 5. Multiply each side by 4. Square each side. Simplify. Free-Fall Height An object is dropped from an unknown height and reaches the ground in 5 seconds. From what height is it dropped? Example 3-1a

  3. Original equation and Check Example 3-1a Answer: The object is dropped from 400 feet.

  4. Free-Fall Height An object is dropped from an unknown height and reaches the ground in 7 seconds. Use the equation to find from what height it is dropped. Answer:784 ft Example 3-1b

  5. Solve Original equation Subtract 8 from each side. Square each side. Add 3 to each side. Example 3-2a Answer: The solution is 52.

  6. Solve Answer:60 Example 3-2b

  7. Solve Original equation Square each side. Simplify. Subtract 2 and add y to each side. Factor. or Zero Product Property Solve. Example 3-3a

  8. Check Example 3-3a Answer: Since –2 does not satisfy the original equation, 1 is the only solution.

  9. Solve Answer:3 Example 3-3b

  10. End of Lesson 3

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