\(\bf c^2=a^2+b^2\qquad
\begin{cases}
c=x\\
a=2\sqrt{2}\\
b=\sqrt{13}
\end{cases}\implies x^2=(2\sqrt{2})^2+(\sqrt{13})^2
\\ \quad \\\\
x^2=2^2\sqrt{2^2}+\sqrt{13^2}\impliedby \textit{with the exponent distributed}
\\\\
x^2=4\cdot 2+13\implies x^2=8+13\implies x^2=21
\\\\
\sqrt{x^2}=\sqrt{21}\impliedby \textit{now, we took }\sqrt{\qquad }\textit{ to both sides}
\\\\
x=\pm \sqrt{21}\)
