Solving Radical Equations Module 14 Topic 4

Audio/Video and Interactive Sites Table of Contents Slides 3-4: How to Solve Radical Equations Slides 5-20: Examples and Practice Problems Slides 21-22: TI Instructions Audio/Video and Interactive Sites Slide 23: Video/Interactive

A radical equation is an equation where there is a variable in the radicand. Radicand: Number or expression under the radical symbol. Examples of Radical Equations: NOT Radical Equations:

How do I solve a radical equation? To solve a radical equation… Isolate the radical to one side of the equation Then raise both sides of the equation to the same power. Simplify Example: Isolate the Radical (subtract 4 from both sides) Raise both Sides to the same power (square both sides)

Equations with Rational Exponents Recall: The square and square root are inverses ( cube and cube root are inverses, and so on.) To solve this equation, you must use the inverse and square both sides. Check your answer.

No Solution Did you check your answers? If so, you seen that in the second problem, q =2 does not work!!!!! Therefore, 2 is an extraneous solution and the solution is “No Solution”

Did you check your answers Did you check your answers? If so, you seen that in the second problem, x= -5 does not work!!!!! Therefore, -5 is an extraneous solution and the solution is x=0. Solution Set { 0 }

Solution Set { 4 }

Equations in the form = k can be solved by raising each side of the equation to the power since . Remember to check for extraneous solutions. Check:

Solution Set { ¼ , 1 }

No Solution The reason is shown below: You can not get a real answer by taking the 4th root of a negative number.

Find the nth root of a if n = 2 and a = 81.

If there are two radicals, isolate both radicals by moving one to the other side of the equal sign. Example: Isolate the radicals Square both sides Simplify Subtract 3x from both sides Add 10 to both sides Divide both sides by 2

I squared both sides, but now I have an x2?! Don’t panic! Continue to solve as a quadratic equation by either using the Quadratic Formula or by Factoring…but you must check for extraneous solutions. When solving radical equations, extra solutions may come up when you raise both sides to an even power.  These extra solutions are called extraneous solutions. Recall, to check for extraneous solutions by plugging in the values you found back into the original problem. If the left side does not equal the right side then you have an extraneous solution. 

Extraneous Solution!

If you have a root other than a square root, simply raise both sides to the same power as the root. So, if you have a cubic root, raise both sides to the third power, for a fourth root, raise both sides to the fourth power, etc. Algebraic Rule for all Radical Equations:

Isolate the radical Cube both sides Simplify Subtract 3 from both sides

Check: Check: This solution does not work, therefore “No Solution”

Check: This solution, -5, does not work, therefore the solution set is { 0 }

Using the TI to solve Simply graph both sides of the equation. The x-values of the intersection point(s) are your solution(s).

Why does the TI only show x = 7? Because 3 is an extraneous solution! Solving Algebraically:

Practice Problems Practice Problems and Answers Examples, Answers, and Videos