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Section 6.6: Solve Radical Equations

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

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Section 6.6: Solve Radical Equations

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

  2. To Solve Radical Equations: • 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.

  3. Ex. √(5x + 1) = 6 √(5x + 1) = 6 (5x + 1)1/2= 6 Rewrite as rational power [(5x + 1)1/2 ]2= 62 Square both sides 5x + 1 = 36 Simplify 5x = 35 Subtract 1 x = 7 Divide by 5 (5(7) + 1)1/2 = 6 Substitute and check. (36)1/2= 6 6=6

  4. EX. 3 √x – 10 = -3 3 √x – 10 = - 3 (x)1/3 – 10 = - 3 Rewrite (x)1/3 = - 3 + 10 Add 10 (x)1/3 = 7 Simplify [(x)1/3]3 = 73 Cube both sides x = 343 Simplify 3 √x – 10 = - 3 Substitute and check 3 √343 – 10 = - 3 7 - 10 = -3 - 3 = - 3

  5. EX. 3x3/2 + 5 = 380 3x3/2 + 5 = 380 3x3/2= 380 – 5 Subtract 5 3x3/2= 375 Simplify x3/2= 375/3 = 125 Divide by 3 and simplify [x3/2]2/3 = 1252/3 Raise both sides the reciprocal power x = 52 = 25 Simplify.

  6. When there are two radicals… 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.

  7. EX. √(x + 6) – 2 = √(x - 2) √(x + 6) – 2 = √(x - 2) [√(x + 6) – 2]2= [√(x - 2) ]2 Square both sides (x + 6) – 4 √(x + 6) + 4 = x – 2 Foil 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 = 3 Divide by (-4) √(x + 6) = 3 Simplify [√(x + 6)]2= (3)2 Square both sides x + 6 = 9 Simplify x = 9 - 6 = 3 Subtract 6

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

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

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