How to Solve Square Roots With Variables
Math students frequently encounter equations to be solved or graphed that include square roots. While the process for solving a problem involving a square root is straightforward, solving square root problems that include variables often appears to be much more complicated. Fortunately, any problem that involves taking the square root of a variable can be solved using principles that are true of all square root problems, regardless of whether they include variables.
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Instructions
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Eliminate the square root sign by squaring both sides of the equation. For example, in an equation with "square root of 4" on the left hand side and "3X" on the other, squaring both sides is the easiest way to eliminate the square root sign. After squaring, 4 would remain on the left hand side and 9X squared on the other side of the equation. Because everything done on one side of an equation must be done on the other, it is not possible to simply square the square root side of the equation.
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Isolate the remaining variable by adding or subtracting to eliminate any numbers from the variable side of the equation. In order to find the values for the variable, it is necessary that the variable be completely isolated on one side of the equation. For instance, in the equation X + 3 = 9, subtracting 3 from both sides of the equation would result in the "X" value being 6.
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Record the value for the isolated variable. Divide both sides of the equation if necessary to separate the variable from any numbers attached to it. For instance, in the equation 3x = 15, the final "X" value will be 5 as the "X" is isolated and solved by dividing both sides of the equation by 3.
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