Question

solve $x^{2} = 24$, 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
o solution.\ $x = \square$

Explanation:

Step1: Take square root of both sides

To solve the equation \(x^{2}=24\) for \(x\) (where \(x\) is a real number), we take the square root of both sides of the equation. Remember that if \(y^{2}=a\) (where \(a\geq0\)), then \(y = \pm\sqrt{a}\). So for \(x^{2}=24\), we have \(x=\pm\sqrt{24}\).

Step2: Simplify the square root

We simplify \(\sqrt{24}\). We can factor \(24\) as \(4\times6\), and since \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we get \(\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}\). Since \(\sqrt{4} = 2\), then \(\sqrt{24}=2\sqrt{6}\). So the solutions for \(x\) are \(x = 2\sqrt{6},- 2\sqrt{6}\).

Answer:

\(2\sqrt{6},-2\sqrt{6}\)