6.4 Solving Radical Equations

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Presentation transcript:

6.4 Solving Radical Equations Objectives: Review solving square root equations Solve equations with other roots

Concept: 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

Review – Solving a Radical Equation 1. Get the radical alone. 2 2 Square both sides to get rid of the square root. ( ) 3. Solve for the variable.

Concept: Solving Other Roots ISOLATE RADICAL / RATIONAL RAISE BOTH SIDES TO RECIPROCAL POWER SOLVE FOR THE VARIABLE

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

EXAMPLE Square both sides. 7x + 2 = 9(3x – 2) Simplify. Solve Square both sides. 7x + 2 = 9(3x – 2) Simplify. 7x + 2 = 27x – 18 Distribute. 20 = 20x Solve for x. 1 = x

Let’s Try Some

Let’s Try Some

Let’s Try Some

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?