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 \( x^2 = 24 \), we take the square root of both sides. Remember that for an equation \( x^2 = a \) (where \( a\geq0 \)), the solutions are \( x=\pm\sqrt{a} \). Here, \( a = 24 \), so we have \( x=\pm\sqrt{24} \).

Step2: Simplify the square root

Simplify \( \sqrt{24} \). We can factor 24 as \( 4\times6 \), and since \( \sqrt{4\times6}=\sqrt{4}\times\sqrt{6} \) (using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) for \( a\geq0,b\geq0 \)), and \( \sqrt{4} = 2 \), so \( \sqrt{24}=2\sqrt{6} \). Thus, the solutions are \( x = 2\sqrt{6},-2\sqrt{6} \).

Answer:

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