Learning Target I CAN solve radical equations Radical

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Learning Target • I CAN solve radical equations.

Learning Target • I CAN solve radical equations.

• Radical Equations – equations that contain radicals in the radicand.

• Radical Equations – equations that contain radicals in the radicand.

Variable as a Radicand FREE-FALL HEIGHT An object is dropped from an unknown height

Variable as a Radicand 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 is height in feet, to find the height from which the object was dropped. Understand You know the time it takes for the object to hit the ground. You need to find the height.

Variable as a Radicand Plan Solve Original equation Replace t with 5. Multiply each

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

Variable as a Radicand Square each side. 400 = h Simplify. Answer: The object

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.

A. 28 ft B. 11 ft C. 49 ft D. 784 ft A. B.

A. 28 ft B. 11 ft C. 49 ft D. 784 ft A. B. C. D. A B C D

Expression as a Radicand Original equation Subtract 8 from each side. Square each side.

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.

A. 64 B. 60 C. 4 D. 196 A. B. C. D. A B

A. 64 B. 60 C. 4 D. 196 A. B. C. D. A B C D

• Extraneous Solutions – when squaring each side of an equation you sometimes

• 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.

Variable on Each Side Check your solution. Original equation Square each side. 2 –

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

Variable on Each Side Check ? ? X Answer: Since – 2 does not

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

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