Question

Rationalize 1/
3+√3​

Answer 1

1/3+√3×3-√3/3-√3

3-√3/(3)^2-(√3)^2

3-√3/9-3

3-√3/6

Answer 2

Answer:

$\frac{3 - \sqrt{3} }{6}$

Step-by-step explanation:

$\frac{1}{3 + \sqrt{3} } \\ \\ = \frac{1}{3 + \sqrt{3} } \times \frac{3 - \sqrt{3} }{3 - \sqrt{3} } \\ \\ = \frac{3 - \sqrt{3} }{(3 + \sqrt{3})(3 - \sqrt{3}) } \\ \\ = \frac{3 - \sqrt{3} }{ {3}^{2} - ( { \sqrt{3} })^{2} } \\ \\ = \frac{3 - \sqrt{3} }{9 - 3} \\ \\ = \frac{3 - \sqrt{3} }{6}$

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