Question

rationalize the denominator 2 + root 3 by 2 minus root 3​

Answer 1

Answer:

Answer = 7+4√3

Step-by-step explanation:

2+√3 / 2-√3

(2+√3)(2+√3) / (2-√3)(2+√3)

(2+√3)^2 / 2^2- (√3)^2

(4+4√3+3) / (4-3)

7+4√3 / 1

= 7+4√3

Answer 2

Step-by-step explanation:

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } \\= \frac{(2 + \sqrt{3}) }{(2 - \sqrt{3}) }\frac{(2 + \sqrt{3}) }{(2 + \sqrt{3}) }\\= \frac{(2 + \sqrt{3})^{2}}{2^{2} - (\sqrt{3})^{2} } \\= \frac{2^{2} + 2.2.\sqrt{3} + (\sqrt{3})^{2}}{4 - 3}\\= \frac{4 + 4\sqrt{3} + 3 }{1} \\= 7 + 4\sqrt{3} (Ans.)$