7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
7­5 Solving Square Root and Other Radical Equations
Objective:
Solve square root and other radical equations.
Jan 29­3:20 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Check Skills You'll Need
Solve by factoring.
1. x2 = ­x + 6
2. x2 = 5x + 14
3. 2x2 + x = 3
4. 3x2 ­ 2 = 5x
5. 4x2 = ­8x + 5
6. 6x2 = 5x + 6
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
A radical equation is an equation that has a variable in the radicand (or a varible with a fractional exponent).
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Solving Square Root Equations
Solve:
2 + √3x - 2 = 6
Step 1: Isolate the radical.
Step 2: Square each side.
Step 3: Solve.
Step 4: Check.
Jan 29­4:07 PM
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7­5 Solving Square Root and Other Radical Equations 2010 Solve:
February 25, 2010
√5x + 1 - 6 = 0
Step 1: Isolate the radical.
Step 2: Square each side.
Step 3: Solve.
Step 4: Check.
Jan 29­4:30 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Solving Radical Equations With Rational Exponents
2(x ­ 2) 2/3 = 50
Divide each side by 2.
(x ­ 2) 2/3 = 25
Raise each side to the 3/2 power.
[(x ­ 2) 2/3]3/2 = (25)3/2
Simplify.
x ­ 2 = √253
x ­ 2 = ±125
x = 127 or x = ­123
Remember there is always a positive and negative square root when SOLVING equations.
CHECK
Jan 29­4:32 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Check:
2(x ­ 2)2/3 = 50
2(127 ­ 2)2/3 = 50
2(x ­ 2)2/3 = 50
2(­123 ­ 2)2/3 = 50
2(53)2/3 = 50 2(­125)2/3 = 50 2(52) = 50
2(­5)2 = 50
50 = 50 50 = 50 Jan 29­5:13 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Solve and Check: 2(x + 3)3/2 = 54
Jan 29­5:09 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Extraneous solutions can be introduced
when you raise both sides of an equation to
a power. So check all possible solutions in
the original equation.
Feb 7­6:09 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Solve √x - 3 + 5 = x.
Then check for extraneous solutions.
Feb 7­6:12 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Solve √5x - 1 + 3 = x.
Then check for extraneous solutions.
Feb 7­6:28 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
Solve (4x ­ 12)1/2 + 3 = x
Then check for extraneous solutions.
Feb 7­6:32 PM
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7­5 Solving Square Root and Other Radical Equations 2010 February 25, 2010
HOMEWORK
p. 394 #1 ­ 12, 15 ­ 20
solve & check all problems
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