QuestionJuly 27, 2025

Rationalize the denominator.Write your answer in exact simplified form. (4)/(sqrt (12))= square

Rationalize the denominator.Write your answer in exact simplified form. (4)/(sqrt (12))= square
Rationalize the denominator.Write your answer in exact simplified form.
(4)/(sqrt (12))= square

Solution
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Answer

\frac{2\sqrt{3}}{3} Explanation 1. Simplify the square root \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}. 2. Rationalize the denominator Multiply numerator and denominator by \sqrt{3}: \frac{4}{2\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{2 \cdot 3}. 3. Simplify the fraction \frac{4\sqrt{3}}{6} = \frac{2\sqrt{3}}{3}.

Explanation

1. Simplify the square root<br /> $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}$.<br />2. Rationalize the denominator<br /> Multiply numerator and denominator by $\sqrt{3}$: $\frac{4}{2\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{2 \cdot 3}$.<br />3. Simplify the fraction<br /> $\frac{4\sqrt{3}}{6} = \frac{2\sqrt{3}}{3}$.
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