Question

Rationalize the denominator
6/2√3+√6​

Answer 1

Step-by-step explanation:

$\frac{6}{2 \sqrt{3} + \sqrt{6} }$

$= \frac{6}{2 \sqrt{3} + \sqrt{6} } \times \frac{2 \sqrt{3} - \sqrt{6} }{2 \sqrt{3} - \sqrt{6} }$

$= \frac{6( 2\sqrt{3} - \sqrt{6} )}{(2 \sqrt{3} + \sqrt{6} )(2 \sqrt{3} - \sqrt{6}) }$

$= \frac{12 \sqrt{3} - 6 \sqrt{6} }{ {(2 \sqrt{3} )}^{2} - {( \sqrt{6}) }^{2} }$

$= \frac{6(2 \sqrt{3} - \sqrt{6} )}{4 \times 3 - 6}$

$= \frac{6(2 \sqrt{3} - \sqrt{6} )}{12 - 6}$

$= \frac{6(2 \sqrt{3} - \sqrt{6} )}{6}$

$= (2 \sqrt{3} - \sqrt{6} )$