The problem is to simplify the expression $\frac{1}{\sqrt{3}}$. We need to rationalize the denominator.

AlgebraRationalizationRadicalsSimplification
2025/3/17

1. Problem Description

The problem is to simplify the expression 13\frac{1}{\sqrt{3}}. We need to rationalize the denominator.

2. Solution Steps

To rationalize the denominator, we multiply both the numerator and denominator by 3\sqrt{3}.
13=1×33×3\frac{1}{\sqrt{3}} = \frac{1 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}
Since 3×3=3\sqrt{3} \times \sqrt{3} = 3, we have:
1×33×3=33\frac{1 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{\sqrt{3}}{3}

3. Final Answer

33\frac{\sqrt{3}}{3}

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