How to Solve Square Radicals
Solving square radicals, or equations that contain the square root of x, is much like solving other kinds of equations. When working with square radicals, as with any kind of equation, you must remember to manipulate both sides of the equation the same way. In addition, focus on eliminating the radical sign in the equation. Keeping these two points in mind, you should not find it difficult to solve these equations.
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Instructions
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Isolate the radical on one side of the equation. For instance, if you have the equation sqrt(x-2)-x=1, add x to both sides of the equation to obtain sqrt(2-x)=x+1.
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Square both sides of the equation to eliminate the radical. Here, the equation becomes 2-x=x2+2x+1.
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Eliminate 2-x from the left side of the equation, so that you can solve the equation like a quadratic equation. Subtracting 2-x from both sides gives 0=x2+3x-1.
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Use the quadratic formula, together with the a, b and c coefficients within the equation, to solve the equation above for the value of x. Since the quadratic formula equals (-b+/- sqrt(b2-4ac))/2a, in which a=1, b=3 and c=-1, plugging into the quadratic formula gives (-3+/-sqrt13)/2. Thus, the quadratic formula gives two values for x: (-3+sqrt13)/2 and (-3-sqrt13)/2.
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