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Solving Radical Equations: Tricks and Checks

Learn how to un-square and un-cube numbers by using square roots and cube roots in equations. Follow the order of operations backward when solving. Be careful of extraneous solutions that may lead to no valid solutions. Practice solving and checking equations step by step.

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Solving Radical Equations: Tricks and Checks

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  1. Section 7.6Solving Radical Equations

  2. Key Ideas • How 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.

  3. Solve and Check! We have to get rid of the square root, so we square both sides. On the left, the square-root and square, cancel out. Add 2 to both sides. Don’t forget to check!

  4. Solve and Check! Add 2 to both sides. Square both sides. Subtract 3. Don’t forget to check!

  5. Solve and Check! Don’t forget to check! That’s not true!

  6. 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.

  7. You Try One!Solve and Check!

  8. Try Another One!Solve and Check

  9. Last One for Now!Solve and Check

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