section 7.6 solving radical equations. key ideas how do you: un-square something? square-root it!...
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Section 7.6Solving Radical Equations
42 x13 2 x
9513 xx
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Key IdeasHow do you:
Un-Square Something? Square-Root it!
Un Cube Something? Cube-Root it!
Un-Square-Root Something? Square it!
Un Cube-Root Something? Cube it!
If you do something to one side of the equation, you have to do that to the other side.
When solving equations, you have to undo the order of operations in the opposite order.
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Solve and Check!42 x
We have to get rid of the square root, so we square both sides.
2242 x
On the left, the square-root and square, cancel out.
162 x Add 2 to both sides. 18x
Don’t forget to check! 4218 416
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Solve and Check!0232 x Add 2 to both sides.
Square both sides.
Don’t forget to check!
232 x
22232 x 432 x
12 x
Subtract 3.
2
1x 023
2
12
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Solve and Check!4415 x 815 x
22815 x 6415 x
655 x 13x Don’t forget to check!
441135 44165 4464
448 412 That’s not true!
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What does this mean?
A solution that doesn’t check is called an “extraneous solution.”
Therefore, the equation we started with has no solutions. Why?
We did all the math correctly, but when we checked our solution, it didn’t work.
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You Try One!Solve and Check!
3112 x
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Try Another One!Solve and Check
8312 xx
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Last One for Now!Solve and Check
13 2 x