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1) When solving radical equations, it is often convenient to square both sides of the equation.
2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation.
Here is a simple example (without radicals): The equation
x = 5
has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get:
x2 = 25
which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
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In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
What are the steps to solving a radical equation?
Details may vary depending on the equation. Quite often, you have to square both sides of the equation, to get rid of the radical sign. It may be necessary to rearrange the equation before doing this, after doing this, or both. Squaring both sides of the equation may introduce "extraneous" roots (solutions), that is, solutions that are not part of the original equation, so you have to check each solution of the second equation, to see whether it is also a solution of the first equation.
How is solving radical equations similar to solving linear equations?
It really is utilized to solve specific variablesIt really is utilized to rearrange the word.
When solving a radical equation you should first isolate the radical and then?
It often helps to square both sides of the equation (or raise to some other power, such as to the power 3, if it's a cubic root).Please note that doing this may introduce additional solutions, which are not part of the original equation. When you square an equation (or raise it to some other power), you need to check whether any solutions you eventually get are also solutions of the original equation.
What property of the square root is essential in order to solve any radical equation involving a square root?
The property that is essential to solving radical equations is being able to do the opposite function to the radical and to the other side of the equation. This allows you to solve for the variable. For example, sqrt (x) = 125.11 [sqrt (x)]2 = (125.11)2 x = 15652.5121
