7.5 Solving Radical Equations

What is a Radical Expression? yes A Radical Expression is an equation that has a variable in a radicand or has a variable with a rational exponent. yes no

EXAMPLE – Solving a Radical Equation 2 2 Square both sides to get rid of the square root ( )

EXAMPLE ( ) 2 2 NO SOLUTION Since 16 doesn’t plug in as a solution. Note: You will get Extraneous Solutions from time to time – always do a quick check Let’s Double Check that this works

Let’s Try Some

Let’s Try Some

SOLVING MORE COMPLEX EQUATIONS + because we are taking an even power (square root) of both sides

RADICAL EQUATIONS ISOLATE RADICAL / RATIONAL RAISE BOTH SIDES TO RECIPROCAL POWER SOLVE FOR THE VARIABLE

SOLVING MORE COMPLEX EQUATIONS Raise each side to the 4th power. This will get you integer powers – much easier to work with! Factor

Let’s Try Some . . . check for extraneous solutions

Let’s Try Some . . . check for extraneous solutions

Can graphing calculators help? SURE! Input for Y1 Input x-2 for Y2 Graph Find the points of intersection One Solution at (4, 2) To see if this is extraneous or not, plug the x value back into the equation. Does it work?