Question

rationalize the denominator of 2+root 3/2-root 3​

Answer 1

Answer:

-(7 + 4√3)

Step-by-step explanation:

2 + √3 / 2 - √3

Multiply and divide by 2 + √3

2 + √3/(2 - √3)    x (2 +√3)/(2 + √3)

= (2 + √3)(2 + √3)/(2 - √3)(2 + √3)

Use (a² - b²) = a² - b²    in denominator    and

(a +b)² = a² + 2ab + b² in numerator

=  (4 + 3 + 4√3)/(2 - 3)

= (7 + 4√3)/(-1)

= -(7 + 4√3)

Answer 2

Answer:

$\frac{7+4\sqrt{3} }{1}$

Step-by-step explanation:

$\frac{2+\sqrt{3} }{2-\sqrt{3} } * \frac{2+\sqrt{3} }{2+\sqrt{3} }$

⇒ $\frac{(2+\sqrt{3})^{2} }{2^{2} - (\sqrt{3}) ^{2} }$

⇒$\frac{2^{2} + (\sqrt{3})^{2} + 2 * 2 * \sqrt{3} }{ 4 - 3}$

⇒$\frac{4 + 3 + 4\sqrt{3} }{1}$

⇒$\frac{7 + 4\sqrt{3} }{1}$