The problem asks us to simplify the expression $\frac{1}{\sqrt{3}}$. This means we need to rationalize the denominator.

ArithmeticRadicalsSimplificationRationalization
2025/3/17

1. Problem Description

The problem asks us to simplify the expression 13\frac{1}{\sqrt{3}}. This means we need to rationalize the denominator.

2. Solution Steps

To rationalize the denominator of 13\frac{1}{\sqrt{3}}, we multiply both the numerator and denominator by 3\sqrt{3}.
13=1333\frac{1}{\sqrt{3}} = \frac{1 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}
Since 33=3\sqrt{3} \cdot \sqrt{3} = 3, we have:
1333=33\frac{1 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{3}}{3}

3. Final Answer

The simplified expression is 33\frac{\sqrt{3}}{3}.

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