Subjects algebra

Simplify Radical D1083A

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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: $$\boxed{2\sqrt{7}}$$