Question

(√2 + √3)(√8 - √12)=??

Answer 1

( √2 + √3) ·( √4√2 - √4√3 ) = 
 =( √2 + √3) ·(2√2  - 2√3) = 
 = ( √2 + √3) · 2 ·( √2 - √3) = 
 = 2 ·[ √2²  - √3² ] = 
 = 2 · ( 2 - 3) = 2 · ( -1 ) = - 2

Answer 2

$( \sqrt{2} + \sqrt{3} )( \sqrt{8} - \sqrt{12} )=( \sqrt{2} + \sqrt{3} )(2 \sqrt{2} -2 \sqrt{3} )= \\ =2 \cdot 2-2 \sqrt{6} +2 \sqrt{6} -2 \cdot 3=4-6=-2$