1. Surd or Radical Equations

2. To solve an equation with a surd First isolate the surd This means to get any terms not under the square root on the other side of the equal sign + 3 2 2 You must square the whole side NOT each term. A square "undoes" or cancels a square root Now square both sides Now solve for x + 1 You MUST check this answer Since you squared both sides of the equation, negatives disappear. It is possible to get an answer that doesn't work when you plug it back in It checks!

3. Let's try another one: First isolate the surd - 1 3 3 Now since it is a 1/3 power this means the same as a cube root so cube both sides Now solve for x - 1 Let's check this answer It checks! Remember that the 1/3 power means the same thing as a cube root. - 1

4. One more to see extraneous solution: The surd is already isolated 2 2 You must square the whole side NOT each term. Square both sides Since you have a quadratic equation (has an x 2 term) get everything on one side = 0 and see if you can factor this You MUST check these answers This must be FOILed Doesn't work! Extraneous It checks! a solution that you find algebraically but DOES NOT make a true statement when you substitute it back into the equation.

5. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au