How to Find Equations of Square Root Functions

In terms of simplifying to solve, equations that involve square root functions are a little different from equations that do not involve square roots. The first problem is that you cannot simply square the side that contains the square roots, as this can actually introduce more square roots. There are ways to solve these equations as long as the equations fulfill certain certain basic requirements.

Instructions

    • 1

      Rearrange equations with a single square root function so the single square root function is on one side of the equal sign and all the other terms are on the other side of the equal sign. Square both sides of the equation. All the terms are now without square root functions, so they can be solved using the normal rules for simplifying equations.

    • 2

      Move both square root terms to the left of the equal sign if there are exactly two square root terms. The square root terms may contain other components such as 5(3)^0.5 or ab(c)^0.5, but that is OK. Square both sides of the equation. There will now be one term on the left of the equal sign that contains a square root function. Keep this single square root function on the left-hand side of the equal sign and move all the other terms to the right side of the equal sign. Square both sides of the equation and there will be no square root functions. You can proceed from here as you would while reducing any equation.

    • 3

      See if your equation fits the model if there are three or more square root functions. These equations can only be solved if there are only square root terms. Even with only square root terms, there must be fewer than five square root terms. If your equation fits this model, arrange the terms so there are no more than two terms on each side of the equal sign. Square both sides of the equal sign. There will now be no more than one square root function on each side of the equal sign, although there will likely be some nonsquare root terms. You can proceed from this point as in the previous steps.

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