Question

Given √3 = 1.782 then find the value of
1+2√3/
2-√3​

Answer 1

Answer:

13.910

Step-by-step explanation:

$\frac{1 + 2 \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\= \frac{2 + \sqrt{3} +( {2 + \sqrt{3} })^{2} }{ {2}^{2} - \sqrt{ {3}^{2} } } \\ = \frac{2 + \sqrt{3 } + ( {2}^{2} + 2 \times 2 \times \sqrt{3} + { \sqrt{3} }^{2} }{4 - 3} \\= \frac{2 + \sqrt{3}+ 4 \sqrt{3} + 3}{1} \\ = \frac{5 + 5 \sqrt{3} }{1}\\ = 5 + 5 \times 1.782 = 5 + 8.310 = 13.910$