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The square root property is a valuable tool for solving quadratic equations. It's used when a variable squared is set equal to a number and you're trying to find the value of the variable. Essentially, the property dictates that if you have an equation in the form \(x^{2} = a\), you can take the square root of both sides to solve for \(x\). This will give you two solutions: \(x = +\sqrt{a}\) and \(x = -\sqrt{a}\). Why two solutions? Because squaring either a positive or a negative number will yield the same positive result. For example, both \(2^2\) and \( (-2)^2\) equal 4.

Applying this to our exercise, when we have the equation \(x^{2} = 16\), using the square root property allows us to deduce that \(x\) must be equal to the square roots of 16. Hence, \(x = \pm4\), since both 4 and -4 squared give 16. Remember, these are considered to be the roots of the equation.

To isolate a variable means to rewrite an equation so that the variable is on one side of the equation and everything else is on the other side. This step is crucial in solving not just quadratic equations, but any algebraic equation. It simplifies the problem and sets the stage for applying further properties or operations to find the variable's value. In our exercise, we began with \(x^{2} - 16 = 0\) and isolated \(x\) by moving the -16 to the other side of the equation, producing \(x^{2} = 16\).

When working with quadratics, the goal is to isolate the squared term to use the square root property effectively. It's like setting the scene for a play; once everything is in its right place, the rest of the process can proceed smoothly. By clearly separating the variable, you pave a clear path toward finding its value.

Quadratic roots are the solutions to quadratic equations, which are equations of the form \(ax^{2} + bx + c = 0\). These roots are where the graph of the equation, a parabola, intersects the x-axis. In mathematical terms, they are the values of \(x\) that make the equation true. There can be two real solutions, one real solution, or two complex solutions, depending on the discriminant \(b^{2} - 4ac\).

In the given exercise, after applying the square root property to \(x^{2} = 16\), we find that the quadratic roots are \(x = 4\) and \(x = -4\). These are the two distinct points where the parabola represented by the equation \(x^{2} - 16 = 0\) would cross the x-axis. In essence, finding the quadratic roots is the end goal when solving quadratic equations because it gives us the values for which the original quadratic equation holds true.