Solving Radical Equations

Solving Radical Equations - Solving Radical Equations Step...

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Solving Radical Equations
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Step 1 : Isolate one of the radicals. , get one radical on one side and everything else on the other using inverse operations. In some problems there is only one radical. However, there are some problems that have more than one radical. In these problems make sure you isolate just one. Step 2 : Get rid of your radical sign. The inverse operation to a radical or a root is to raise it to an exponent. Which exponent? Good question, it would be the exponent that matches the index or root number on your radical. In other words, if you had a square root, you would have to square it to get rid of it. If you had a cube root, you would have to cube it to get rid of it, and so forth. You can raise both sides to the 2nd power, 10th power, hundredth power, etc. As long as you do the same thing to both sides of the equation, the two sides will remain equal to each other. Step 3 : If you still have a radical sign left, repeat steps 1 and 2. Sometimes you start out with two or more radicals in your equation. If that is the case and you have at least one nonradical term, you will probably have to repeat steps 1 and 2. Step 4 : Solve the remaining equation. The equations in this tutorial will lead to either a linear or a quadratic equation. If you need a review on solving linear equations, feel free to go to Tutorial 14: Linear Equations in One Variable . If you need a review on solving quadratic equations, feel free to go to Tutorial 17: Quadratic Equations . Step 5 : 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. If a value is an extraneous solution, it is not a solution to the original problem. In radical equations, you check for extraneous solutions by plugging in the values you found
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Example 1 : Solve the radical equation . View a video of this example Step 1 : Isolate one of the radicals. The radical in this equation is already isolated. Step 2 : Get rid of your radical sign. If you square a square root, it will disappear. This is what we want to do here so that we can get x out from under the square root and continue to solve for it. *Inverse of taking the sq. root is squaring it Step 3 : If you still have a radical left, repeat steps 1 and 2. No more radicals exist, so we do not have to repeat steps 1 and 2.
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Step 4 : Solve the remaining equation. In this example, the equation that resulted from squaring both sides turned out to be a linear equation . If you need a review on solving linear equations, feel free to go to Tutorial 14: Linear Equations in One Variable . *Inverse of add. 5 is sub. 5 *Inverse of mult. by 2 is div. by 2 Step 5 : Check for extraneous solutions. Let's check to see if
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This note was uploaded on 02/18/2011 for the course MATH 101 taught by Professor Kindle during the Spring '11 term at South Texas College.

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Solving Radical Equations - Solving Radical Equations Step...

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