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Quadratic equations are mathematical expressions where the highest power of the variable is squared (i.e., the variable is raised to the power of two). A general form of a quadratic equation is written as: \[ax^2 + bx + c = 0\].To solve these types of equations, one of the methods we use is the Square Root Property. This property is particularly useful when the quadratic equation does not have a linear term (where \(b = 0\)). For example, in the quadratic equation given in the problem, \(x^2 = 2.25\), we can directly apply the Square Root Property.

Simplifying radicals is an essential step in solving equations involving square roots. In the context of solving equations using the Square Root Property, we often encounter radicals that need to be simplified for a clear and concise solution. Simplifying a radical involves expressing the number under the square root as a product of a perfect square and another factor. For example:Since \(2.25\) can be written as \(1.5^2\), the simplification of \(\sqrt{2.25}\) becomes straightforward: \(\sqrt{2.25} = \sqrt{1.5^2} = 1.5\). We must remember to consider both the positive and negative roots when solving quadratic equations using square roots. Thus, solving for \(x\) yields \( x = \pm 1.5\).

Square roots are inverse operations to squaring a number. When you have the equation \(x^2 = k\), taking the square root on both sides will help us find the value of \(x\). The square root of a number \(k\) is any number that, when multiplied by itself, gives the value \(k\). The symbol for the square root is \(\sqrt{ }\). For example:When we say \(\sqrt{16} = 4\), it means that \(4^2 = 16\).Consider the problem \(x^2 = 2.25\): Taking the square root of both sides, we get \(x = \pm \sqrt{2.25}\). After simplifying the radical, as we've seen earlier, we get the values \(x = \pm 1.5\). This means our solutions are \(x = 1.5\) and \(x = -1.5\). Understanding how to find and work with square roots is crucial for solving many types of equations, especially quadratics.