Given <span class="math-tex">\(\sqrt {(224)_r}=(13)_r\)</span>, then the value of the radix is
\((224)_r = 2r^2 + 2r + 4\) and \((13)_r = r + 3\).
\((r + 3)^2 = 2r^2 + 2r + 4 \Rightarrow r^2 - 4r - 5 = 0 \Rightarrow (r - 5)(r + 1) = 0\)
A radix must be positive, so \(r = 5\).
Answer: (C) 5
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