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Section 6.6: Solve Radical Equations Starter: CC 6.5 Part 2

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Before beginning, it may be easier to rewrite as rational exponents. Step 1) Isolate the radical. Get the radical by itself Step 2) Raise both sides to the reciprocal power √x use (√x) 2, 3 √x use ( 3 √x) 3 Step 3) Simplify, use foil if necessary Step 4) Solve for the variable. Step 5) Check all solutions, some may be extraneous. To Solve Radical Equations:

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√(5x + 1) = 6 (5x + 1) 1/2 = 6Rewrite as rational power [(5x + 1) 1/2 ] 2 = 6 2 Square both sides 5x + 1 = 36Simplify 5x = 35Subtract 1 x = 7Divide by 5 (5(7) + 1) 1/2 = 6Substitute and check. (36) 1/2 = 6 6=6 Ex. √(5x + 1) = 6

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3 √x – 10 = - 3 (x) 1/3 – 10 = - 3Rewrite (x) 1/3 = - 3 + 10Add 10 (x) 1/3 = 7Simplify [(x) 1/3 ] 3 = 7 3 Cube both sides x = 343Simplify 3 √x – 10 = - 3Substitute and check 3 √343 – 10 = - 3 7 - 10 = -3 - 3 = - 3 EX. 3 √x – 10 = -3

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3x 3/2 + 5 = 380 3x 3/2 = 380 – 5Subtract 5 3x 3/2 = 375Simplify x 3/2 = 375/3 = 125Divide by 3 and simplify [x 3/2 ] 2/3 = 125 2/3 Raise both sides the reciprocal power x = 5 2 = 25Simplify. EX. 3x 3/2 + 5 = 380

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Step 1) Isolate one radical Step 2) Raise both sides to the reciprocal power Step 3) Simplify Step 4) Isolate the other radical Step 5) Raise to the reciprocal power Step 6) Solve by simplifying. When there are two radicals…

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√(x + 6) – 2 = √(x - 2) [√(x + 6) – 2] 2 = [√(x - 2) ] 2 Square both sides (x + 6) – 4 √(x + 6) + 4 = x – 2Foil the left, simplify the right x + 10 – 4 √(x + 6) = x – 2 Simplify and isolate the radical -4√(x + 6) = x – 2 – (x + 10)Subtract (x + 10) √(x + 6) = -12/-4 = 3Divide by (-4) √(x + 6) = 3Simplify [√(x + 6)] 2 = (3) 2 Square both sides x + 6 = 9Simplify x = 9 - 6 = 3Subtract 6 EX. √(x + 6) – 2 = √(x - 2)

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√(3 + 6) – 2 = √(3 - 2)Substitute and check √9 – 2 = √1 3-2 = 1 1 = 1 Always Check your answers!

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456: A: 3, 7, 9, 13, 15, 17, 23, 25 B: 11, 19, 21, 25, 27, 37 C: 18, 26, 28, 38, 42 Your Turn:

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