Question

solve $x^2 = 54$, 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 \( x^2 = 54 \), we take the square root of both sides. Remember that for any real number \( a \), if \( x^2 = a \), then \( x=\pm\sqrt{a} \) (when \( a\geq0 \)). Here, \( a = 54\geq0 \), so we have \( x=\pm\sqrt{54} \).

Step2: Simplify the square root

Simplify \( \sqrt{54} \). We can factor 54 as \( 9\times6 \), and since \( \sqrt{9\times6}=\sqrt{9}\times\sqrt{6} \) (by the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) for \( a\geq0,b\geq0 \)), and \( \sqrt{9} = 3 \), so \( \sqrt{54}=3\sqrt{6} \). Thus, \( x = \pm3\sqrt{6} \), which means \( x = 3\sqrt{6}, - 3\sqrt{6} \).

Answer:

\( 3\sqrt{6}, - 3\sqrt{6} \)