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Solving Radical Equations

This guide will teach you how to solve radical equations efficiently. A radical equation includes square roots, and to solve it, we aim to isolate the variable. The key steps include simplifying the expression, isolating the radical, squaring both sides, and finally, solving the resulting equation. Be cautious of extraneous solutions that do not satisfy the original equation. By following the outlined steps, you can navigate through radical equations with confidence.

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Solving Radical Equations

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  1. Solving Radical Equations

  2. A radical equation is an equation that contains a radical. BACK

  3. The goal in solving radical equations is the same as the goal in solving most equations. BACK

  4. We need to isolate the variable. BACK

  5. But there is only one way to move the variable out from under the square root sign. BACK

  6. We need to square the radical expression. BACK

  7. And, because it is an equation, what we do to one side, BACK

  8. And, because it is an equation, what we do to one side, we have to do to the other. BACK

  9. Remember, no matter what n is. (Even if n is an expression) BACK

  10. So we have: BACK

  11. Solve for x: Step 1. Simplify the expression: BACK

  12. Solve for x: BACK

  13. Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. BACK

  14. Solve for x: BACK

  15. Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. Step 3. Square both sides. BACK

  16. Solve for x: BACK

  17. Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. Step 3. Square both sides. Step 4. Solve the equation. BACK

  18. Solve for x: BACK

  19. Dude! You try one. Try this one: BACK

  20. BACK

  21. BACK

  22. Dude! You try one. Try this one: BACK

  23. No Solutions If you have a square root equaling a negative number there is no solution.

  24. An Extraneous Solution is a solution that does not satisfy the original equation. -2 is an extraneous answer.

  25. Watch Out!! If all answers are extraneous, there is also no solution.

  26. Since -11 does not satisfy the original equation, 11 is the only solution. -11 is an extraneous solution. Is this a true statement?

  27. Solving Radical Equations BACK

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