Section 7.6 Solving Radical Equations  The Power Principle for Equations If A = B then A n = B n  The Danger in Solving an Equivalent Equation  Equations Containing One Radical  Equations Containing Two Square Roots 7.61

Definitions  A Radical Equation must have at least one radicand containing a variable  The Power Rule:  If we raise two equal expressions to the same power, the results are also two equal expressions  If A = B then A n = B n for any n  Warning: These are NOT equivalent Equations! When n is even, you MUST check answers in the original equation 7.62

Why are they not Equivalent?  Start with a simple original equation:  x = 3  Square both sides to get a new equation:  x 2 = 3 2 which simplifies to x 2 = 9  x 2 = 9 has two solutions x = 3 and x = -3  Checking solutions in the original x = 3: 3 = 3 is true, so x = 3 is OK -3 = 3 is untrue, so discard x =

Equations Containing One Radical  To eliminate the radical, raise both sides to the index of the radical 7.64

Sometimes, You Need to Isolate the Radical  Get the radical alone before raising to a power 7.65

More Examples

More Examples

More Examples

More Examples

Equations Containing Two Radicals  Make sure radicals are on opposite sides  Sometimes you need to repeat the process 7.610

What Next? Complex Numbers!  Present Section 7.8 Present Section 7.8  7.7 Is Not Covered 7.611