Question

Rationalise the denominator of 2+√3 / 2-√3​

Answer 1

Step-by-step explanation:

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{ 2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ = \frac{(2 + \sqrt{3} {)}^{2} }{ {2}^{2} - { \sqrt{3} }^{2} } \\ \\ = \frac{ {2}^{2} + { \sqrt{3} }^{2} + 2 \times 2 \times \sqrt{3} }{4 - 3} \\ \\ = \frac{4 + 3 + 4 \sqrt{3} }{1} \\ \\ = 7 + 4 \sqrt{3}$

Answer 2

Answer:

(7 + 4√3)

Step-by-step explanation:

(2+√3 / 2-√3) × (2+√3 / 2+√3)

= (2+√3)^2 / (4-3)

= (4+3+4√3)/1

= (7 + 4√3)