Questions: Quadratic Equations and Functions Solving a quadratic equation using the square root property: Exact.: Solve (x^2=48), where (x) is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas If there is no solution, click "No solution." [ x= ] (sqrtsquare)

Solution Steps

To solve the quadratic equation \(x^2 = 48\) using the square root property, we take the square root of both sides of the equation. This will yield two solutions: one positive and one negative, since both \((\sqrt{48})^2\) and \((- \sqrt{48})^2\) equal 48. We then simplify the square root of 48 to its simplest radical form.

We start with the equation \(x^2 = 48\). To find the values of \(x\), we apply the square root property:

\[ x = \pm \sqrt{48} \]

Next, we simplify \(\sqrt{48}\). We can express 48 as \(16 \times 3\):

\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \]

Thus, the solutions can be rewritten as:

\[ x = \pm 4\sqrt{3} \]

Calculating the numerical values, we find:

\[ 4\sqrt{3} \approx 6.9282 \]

Therefore, the solutions are:

\[ x \approx 6.9282 \quad \text{and} \quad x \approx -6.9282 \]

Final Answer