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The square root property is a useful tool for solving quadratic equations. A quadratic equation typically takes the form of o[n] = ax^2 + bx + c = 0, but to use the square root property effectively, it's best if the term with the variable squared is isolated. The property itself states that if we have an equation of the form:o[n] = t^2 = k = 0,then the solutions for t are:o[n] = t = ± √k.In the context of our example, we have o[n] = t^2 = 48.By applying the square root property, we get:o[n] = t = ± √48.This tells us that t can be either the positive or negative square root of 48.

The next step in solving the quadratic equation is simplifying the radical. When you take the square root of a number, the result is known as a 'radical'. Simplifying this radical makes solving the equation simpler. Let's take a look on how to simplify o[n] = √48.First, we break down 48 into its prime factors to make simplification easier. The prime factorization of 48 is:o[n] = 48 = 16 × 3 = 4^2 × 3.Now, recall that when you take the square root of a product, it's equivalent to taking the square root of each factor. That means we can simplify as follows:o[n] = √48 = √(4^2 × 3) = 4√3.So, o[n] = √48 = 4√3.By simplifying o[n] = √48,we get: o[n] = ± 4√3. This makes our equation much neater and easier to work with.

Before applying the square root property, always ensure the square term is isolated on one side of the equation. This greatly simplifies further steps. Let's discuss how to isolate the square term.Given the equation: o[n] = t^2 = 48,we can see that the square term o[n] = t^2 is already isolated. Isolation means having the o[n] = t^2 term by itself on one side of the equation, with a constant or zero on the other side. If the original equation includes extra variables or numbers on the same side as the squared term, moving these terms to the other side of the equation by adding or subtracting will isolate the squared term. For example, for an equation like o[n] = t^2 + 5 = 53,we isolate o[n] = t^2 by subtracting 5 from both sides, yieldingo[n] = t^2 = 48.Once the square term is isolated, you can proceed with the square root property and any necessary radical simplification.