Question

how to rationalize it?
$\frac{1}{2} \times \frac{ \sqrt{3} }{2( 1+ \sqrt{3}) }$​

Answer 1

Answer:

$\frac{ 3 - \sqrt{3} }{8}$

Step-by-step explanation:

$\frac{1}{2} \times \frac{ \sqrt{3} }{2 \times (1 + \sqrt{3)} } \\ \\ = \frac{1}{4} \times \frac{ \sqrt{3}( { }1 - \sqrt{3)} }{ {1}^{2} - {( \sqrt{3} )}^{2} } \\ \\ = \frac{1}{4} \times \frac{ \sqrt{3} - 3}{(1 - 3)} \\ \\ = \frac{ \sqrt{3 } - 3}{-8}$

Answer 2

Here's your answer :-

• Question :-

$\frac{1}{2} \times \frac{ \sqrt{3} }{2( 1+ \sqrt{3}) }$

• Solution :-

$= > \frac{1}{2} \times \frac{ \sqrt{3} }{2(1 + \sqrt{3} )}$

$= > \frac{ \sqrt{3} }{4(1 + \sqrt{3})}$

$= > \frac{ \sqrt{3} }{4} \times ( \frac{1}{1 + \sqrt{3} })$

• Now, keep √3/4 aside for a minute and rationalize by 1/1+√3 in both numerator and denominater.

$= > \frac{1 - \sqrt{3} }{(1 + \sqrt{3})(1 - \sqrt{3})} = \frac{1 - \sqrt{3} }{(1 - 3)}$

• Now, multiply √3/4 by the following :-

$= > \frac{ \sqrt{3} \times(1 - \sqrt{3})}{4(1 - 3)}$

$= > \frac{ \sqrt{3} - 3 }{4( - 2)}$

• Take -ve sign common outside the parenthesis.

$= > \frac{ - ( - \sqrt{3} - + 3)}{ - (8)}$

$= > \frac{3 - \sqrt{3} }{8}$

Hope it helps!

~ A.R.M.Y ♡ ~