Simplify \({4}^{2}\) to \(16\).
\[16+{5}^{2}+{z}^{2}={21}^{2}\]
Simplify \({5}^{2}\) to \(25\).
\[16+25+{z}^{2}={21}^{2}\]
Simplify \({21}^{2}\) to \(441\).
\[16+25+{z}^{2}=441\]
Simplify \(16+25+{z}^{2}\) to \({z}^{2}+41\).
\[{z}^{2}+41=441\]
Subtract \(41\) from both sides.
\[{z}^{2}=441-41\]
Simplify \(441-41\) to \(400\).
\[{z}^{2}=400\]
Take the square root of both sides.
\[z=\pm \sqrt{400}\]
Since \(20\times 20=400\), the square root of \(400\) is \(20\).
\[z=\pm 20\]
z=20,-20
