section 7.6 solving radical equations. key ideas how do you: un-square something? square-root it!...

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Section 7.6 Solving Radical Equations 4 2 x 1 3 2 x 9 5 1 3 x x

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Page 1: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

Section 7.6Solving Radical Equations

42 x13 2 x

9513 xx

Page 2: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

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.

Page 3: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

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

Page 4: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

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

Page 5: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

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!

Page 6: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

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.

Page 7: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

You Try One!Solve and Check!

3112 x

Page 8: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

Try Another One!Solve and Check

8312 xx

Page 9: Section 7.6 Solving Radical Equations. Key Ideas How do you: Un-Square Something?  Square-Root it! Un Cube Something?  Cube-Root it! Un-Square-Root

Last One for Now!Solve and Check

13 2 x