Solving Radical Equations

• Radical equation


  An equation with one unknown in one or more of the radicals
• Solving radical equations

  1. Isolate the radical term

  2. Square both sides of the equation

  3. Check if all radicals have been eliminated

  4. If radicals remain, repeat the process
• Solving the example radical equation


  1. Isolate the radical term by subtracting 1

  2. Square both sides

  3. Simplify to get x = 16
• Checking the solution

  Substitute x = 16 back into the original equation to verify
• Solving the example radical equation

  1. Isolate the radical term

  2. Cube both sides

  3. Simplify to get x = 65
• Checking the solution

  Substitute x = 65 back into the original equation to verify
• Solving the example radical equation

  1. Cube both sides

  2. Combine like terms

  3. Solve for x = -3
• Checking the solution

  Substitute x = -3 back into the original equation to verify
• Solving the example radical equation


  1. Square both sides

  2. Simplify to get x = 1
• Checking the solution

  Substitute x = 1 back into the original equation to verify that there is no real solution
• Right triangle


  A triangle with one 90 degree angle
• Finding the length of the legs of a right triangle

  1. Use the Pythagorean Theorem: a^2 + b^2 = c^2, where c is the hypotenuse

  2. Substitute the given hypotenuse length of 5 square root of 2

  3. Solve for the length of each leg, which is 5 units