Question

simplify the expression two +root 3 /2-root 4

Answer 1

here is your answer

Answer 2

$\textbf{Answer :-}$

_______________________________

To Simplify :- $\mathsf{\frac{2+\sqrt{3}}{2-\sqrt{3}}}$

Salutation :-

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

= $\mathsf{\frac{( 2 + \sqrt{3} ) ( 2 + \sqrt{3} )}{( 2 - \sqrt{3} ) ( 2 + \sqrt{3} )}}$

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

= $\mathsf{\frac{4 + 4\sqrt{3} + 3}{4 - 3}}$

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

= $\mathsf{7 + 4\sqrt{3}}$ [ Required answer ]

__________________________________