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Simplify: 3+2sqrt(3) / sqrt(3)

June 4, 2026Mathematics

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Answer

2+\sqrt{3}

4 steps

To simplify the expression, we need to rationalize the denominator by multiplying both the numerator and the denominator by $\sqrt{3}$ .

Write the given expression.
$\frac{3+2\sqrt{3}}{\sqrt{3}}$
Multiply the numerator and denominator by $\sqrt{3}$ .
$\frac{3+2\sqrt{3}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$
Distribute $\sqrt{3}$ in the numerator and simplify the denominator.
$\frac{3\sqrt{3} + 2\sqrt{3}\sqrt{3}}{3}$ $\frac{3\sqrt{3} + 2(3)}{3}$ $\frac{3\sqrt{3} + 6}{3}$
Separate the terms and simplify.
$\frac{3\sqrt{3}}{3} + \frac{6}{3}$ $\sqrt{3} + 2$
The simplified expression is:
$2+\sqrt{3}$

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