radicals 2 solving radical equations...09 radicals2 solvingradicalequations notes.notebook 1 january...
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09 Radicals2SolvingRadicalEquations Notes.notebook
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Radicals 2 Solving Radical Equations
Standard: AREI.2 Math Practice: Look for and make use of structureGLOs: #3Complex ThinkerHW: WS#8Learning Target: • How do you solve a radical equation?• How do you know if the solution is extraneous?
09 Radicals2SolvingRadicalEquations Notes.notebook
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Warm Up: Solve for x:a) b)
09 Radicals2SolvingRadicalEquations Notes.notebook
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In this unit, we will examine how to solve square root equations. These are equations that have x inside a square root
Steps to Solve a Radical Equation:1. Get the square root expression by itself on one side of the equation
2. Square both sides (to cancel out the radical)
3. Solve the remaining equation using previously learned techniques (typically those involving linear or quadratic equations).
4. Check your solution(s)!*
Whenever you square both sides of an equation, you technically get a new (but related) equation. And sometimes, when you do this, you obtain a solution that may work for the “new” equation, but does not work for the original equation. Such answers are
called extraneous solutions .
So ALWAYS check your answers!
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Example 1: Solve for x:
Check:
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Jan 297:31 AM
Practice: Solve for x:
a) b)
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Practice: Solve for x:
c) d)
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Example 2: Solve for x:
Check:
Don’t forget, before you can square both sides, isolate the radical to one side!
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Practice: Solve for x:
e) f)
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Example 3: Solve for x:
Check:
Some equations have two square roots. In these cases rearrange the equation to get one square root on each side of the equation, then square both sides.
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Practice: Solve for x:
g) h)
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Example 4: Solve for x:
Check: and
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Practice: Solve for x:
i) j)