Solving Radical Equations The Power Rule Equations Containing One Radical

Definitions A Radical Equation must have at least one radicand containing a variable The Power Rule: If we raise two equal quantities to the same power, the results are also two equal quantities If x = y then xn = yn Warning: These are NOT equivalent Equations!

Why are they not Equivalent? Start with a simple original equation: x = 3 Square both sides to get a new equation: x2 = 32 which simplifies to x2 = 9 The only solution to x = 3 is 3 x2 = 9 has two solutions 3 and -3 Raising both sides of the equation to an equal power is called an irreversible step. Therefore we need to check our solutions to make sure they are valid.

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

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

Practice – on the board

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

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

Practice – on the board

What Next? Homework Worksheet