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Solving Radical Equations
Brett Solberg AHS β11-β12
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Warm-up Write with rational exponents 1) 7 π₯ 3 π¦ 2 π§ 2 2) 3ππ 3
1) 7 π₯ 3 π¦ 2 π§ 2 2) 3ππ 3 3) Solve for x x2 + 6x + 8 = 0 What HW problems should we review?
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Todayβs Agenda HW Review Solving Radicals
Isolating Radicals Get out your notes and extra paper
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The Principle of Powers
If x = 5 Then x2 = 52 If π₯ = 5 Then ( π₯) 2 = 52 If βπ₯ = x + 5 Then ( 2 βπ₯ )2 = (x + 5)2
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Steps to Solving Radical Expressions
Isolate the radical Rationalize the radical Solve Check your work π₯ - 3 = 4 π₯ = 7 Isolate the radical ( π₯ )2 = Rationalize the radical x = 49 Solve = 4 Check your work 7 β 3 = 4 4 = 4
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Examples π₯ - 7 = 3 3π₯+4 = 5
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Extraneous Roots x = π₯+7 + 5 Why did one of the solutions not work?
Solutions that donβt check are called extraneous solutions
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x β 5 = 18 β2π₯ x β 2 = 2π₯ β1
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What if thereβs more than one radical?
Plan A β Combine Radicals 3 π₯ = 2 π₯ - 1
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What if thereβs more than one radical?
Plan B β Solve one radical at a time 3 π₯ = 2 π₯ - 1
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π₯ β π₯ = 1
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Other Radicals 3 π₯ = 5 3 π₯ β = 7
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Beach If I stand on the beach, how far can I see? d = 1.2 β
d = distance miles h = height in feet
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Summary Isolate Rationalize Solve Check
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Homework 7.6 pg 319 #1 β 33, 43 β 45 Midyear Review:
going on this quarter correct it in class on Thu
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