Answer
$\left\{\pm3\sqrt{6}\right\}$
Work Step by Step
Taking the square root of both sides (Square Root Property), the given equation, $
t^2=54
,$ is equivalent to
\begin{align*}
t&=\pm\sqrt{54}
.\end{align*}
Using the properties of radicals, the equation above is equivalent to
\begin{align*}\require{cancel}
t&=\pm\sqrt{9\cdot6}
\\
t&=\pm\sqrt{9}\cdot\sqrt{6}
\\
t&=\pm3\sqrt{6}
.\end{align*}
Hence, the solution set of $
t^2=54
$ is $
\left\{\pm3\sqrt{6}\right\}
$.
