Question

Rationalise the denominator 3/2-√3

Answer 1

$HEYA \: \\ \\ GIVEN \: QUESTION \: Is \: \\ \\ \frac{3}{2 - \sqrt{3} } \\ \\ multiply \: Numerator \: \: and \: \: Denominator \: \\ \: by \: \: 2 + \sqrt{3} \\ \\ \frac{3}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \frac{3(2 + \sqrt{3}) }{2 {}^{2} - ( \sqrt{3} ) {}^{2} } \: \: \: \: \: \\ \\ \frac{6 + 3 \sqrt{3} }{4 - 3} \\ \\ \frac{6 + 3 \sqrt{3} }{1} \\ \\ = 6 + 3 \sqrt{3}$

Answer 2

Step-by-step explanation:

$\begin{lgathered} \frac{3}{2 - \sqrt{3} } \\ \\ Multiply \: Numerator \: \: And \: \: Denominator \: \\ \: By \: \: 2 + \sqrt{3} \\ \\ \frac{3}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \frac{3(2 + \sqrt{3}) }{2 {}^{2} - ( \sqrt{3} ) {}^{2} } \: \: \: \: \: \\ \\ \frac{6 + 3 \sqrt{3} }{4 - 3} \\ \\ \frac{6 + 3 \sqrt{3} }{1} \\ \\ = 6 + 3 \sqrt{3}\end{lgathered} </p><p>$