1. The problem asks to simplify the expression $$\frac{\sqrt{252}}{3}$$ in simplest radical form.
2. First, factorize 252 to find perfect squares inside the square root:
$$252 = 4 \times 63 = 4 \times 9 \times 7$$
3. Use the property of square roots that $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$:
$$\sqrt{252} = \sqrt{4 \times 9 \times 7} = \sqrt{4} \times \sqrt{9} \times \sqrt{7}$$
4. Calculate the square roots of perfect squares:
$$\sqrt{4} = 2, \quad \sqrt{9} = 3$$
5. Substitute back:
$$\sqrt{252} = 2 \times 3 \times \sqrt{7} = 6\sqrt{7}$$
6. Now substitute into the original expression:
$$\frac{\sqrt{252}}{3} = \frac{6\sqrt{7}}{3}$$
7. Simplify the fraction by canceling common factors:
$$\frac{\cancel{6}\sqrt{7}}{\cancel{3}} = 2\sqrt{7}$$
8. Final answer:
$$\boxed{2\sqrt{7}}$$
Simplify Radical D1083A
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