To rationalize the denominator of the expression \(\frac{2 + \sqrt{3}}{\sqrt{3}}\), we can multiply the numerator and the denominator by \(\sqrt{3}\). Here are the steps:
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Start with the expression: \[ \frac{2 + \sqrt{3}}{\sqrt{3}} \]
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Multiply both the numerator and the denominator by \(\sqrt{3}\): \[ \frac{(2 + \sqrt{3}) \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} \]
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Simplify the denominator: \[ \sqrt{3} \cdot \sqrt{3} = 3 \]
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Distribute \(\sqrt{3}\) in the numerator: \[ (2 + \sqrt{3}) \cdot \sqrt{3} = 2\sqrt{3} + 3 \]
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Now, we can write the full simplified expression: \[ \frac{2\sqrt{3} + 3}{3} \]
So, the expression \(\frac{2 + \sqrt{3}}{\sqrt{3}}\) rationalized is: \[ \frac{2\sqrt{3} + 3}{3} \]