Question

Simplify 2√6 ÷ 3+√3 by rationalizing the denominator

Answer 1

Answer:

√2(√3 - 1)

Step-by-step explanation:

$\frac{2 \sqrt{6} }{3 + \sqrt{3} } \\ = \frac{2 \sqrt{6} }{3 + \sqrt{3} } \times \frac{3 - \sqrt{3} }{3 - \sqrt{3} } \\ = \frac{2 \sqrt{6}(3 - \sqrt{3} ) }{9 - 3} \\ = \frac{6 \sqrt{6} - 2 \sqrt{18} }{6} \\ = \frac{6 \sqrt{6} - 6 \sqrt{2} }{6} \\ = \sqrt{6} - \sqrt{2} \\ = \sqrt{2} ( \sqrt{3} - 1)$

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