Question

2+square root of 3 / 2 - square root of 3=?

Answer 1

Question: $\dfrac{2 + \sqrt{3}}{2 - \sqrt{3}}$

Answer: 7 + 4√3

Step-by-step explanation:

This question can be solved by rationalising it's denominator.

$\sf \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \\ \\ \sf \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \sf \frac{(2 + \sqrt{3}) {}^{2} }{(2) {}^{2} - ( \sqrt{3}) {}^{2}} \\ \\ \sf \frac{(2)^{2} + ( \sqrt{3})^{2} + 2 \times 2 \times \sqrt{3} }{4 - 3} \\ \\ \sf \frac{4 + 3 + 4 \sqrt{3} }{1} \\ \\ \boxed{ \red{ \bf 7 + 4 \sqrt{3}}}$

Hence, the answer is 7 + 4√3.

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Identity Used ;

1. (a + b)² = a² + b² + 2ab
2. (a + b)(a - b) = a² - b²