To simplify \(252\) into one of the given options, we will first factor \(252\) and then compare it with the choices.
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Factor \(252\): \(252 = 2^2 \times 3^2 \times 7\).
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Calculate each option:
a. \(6 \sqrt{7}\): \[ (6 \sqrt{7})^2 = 6^2 \times 7 = 36 \times 7 = 252 \] So, \(6 \sqrt{7}\) represents \(\sqrt{252}\).
b. \(21 \sqrt{63}\): First, simplify \(63 = 9 \times 7 = 3^2 \times 7\): \[ 21 \sqrt{63} = 21 \sqrt{9 \times 7} = 21 \times 3 \sqrt{7} = 63 \sqrt{7}. \] \[ (63 \sqrt{7})^2 = 63^2 \times 7 = 3969 \times 7 \neq 252. \]
c. \(12 \sqrt{21}\): \[ (12 \sqrt{21})^2 = 12^2 \times 21 = 144 \times 21 = 3024 \neq 252. \]
d. \(3 \sqrt{28}\): Since \(28 = 4 \times 7 = 2^2 \times 7\): \[ (3 \sqrt{28})^2 = 3^2 \times 28 = 9 \times 28 = 252. \]
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Summary of results:
- \(6 \sqrt{7}\) yields \(\sqrt{252}\).
- \(21 \sqrt{63}\) is not valid.
- \(12 \sqrt{21}\) is not valid.
- \(3 \sqrt{28}\) yields \(\sqrt{252}\).
From the options, both \(6 \sqrt{7}\) and \(3 \sqrt{28}\) are valid simplifications of \(\sqrt{252}\).
However, \(6 \sqrt{7}\) is the simplest representation of \(252\) since we are looking for a direct correlation to what \(252\) simplifies to.
Thus the correct and simplest answer is: \[ \boxed{6 \sqrt{7}}. \]