Question

Simplify
√2(√6 - √8) + √3(√27 - √6)

Answer 1

$\sqrt{2} ( \sqrt{6} - \sqrt{8} ) + \sqrt{3} ( \sqrt{27} - \sqrt{6} ) \\ \\ \\ Open \: \: brackets , \\ \\ \\ = >( \sqrt{6} \times \sqrt{2} ) - ( \sqrt{8} \times \sqrt{2} ) + ( \sqrt{3} \times \sqrt{27}) - ( \sqrt{6} \times \sqrt{3} )$ $\\ \\ \\ \\ = > \sqrt{6 \times 2} - \sqrt{8 \times 2} + \sqrt{3 \times 27} - \sqrt{6 \times 3} \\ \\ \\ \\ = > \sqrt{3 \times 2 \times 2} - \sqrt{2 \times 2 \times 2 \times 2} + \sqrt{3 \times 3 \times 3 \times 3} - \sqrt{2 \times 3 \times 3} \\ \\ \\ \\ = > 2 \sqrt{3} - (2 \times 2) + (3 \times 3) - 3 \sqrt{2} \\ \\ \\ \\ = > 2 \sqrt{3} - 4 + 9 - 3 \sqrt{2} \\ \\ \\ \\ = > 2 \sqrt{3} + 5 - 3 \sqrt{2}$

Answer 2

SOLUTION:

$= \bf \: \sqrt{2} ( \sqrt{6} - \sqrt{8} ) + \sqrt{3} ( \sqrt{27} - \sqrt{6} )$

On solving brackets we get,

$= \: \bf \: \sqrt{2} ( \sqrt{2} ) \: + \: \sqrt{3} ( \sqrt{21} ) \\ \\ = \: \bf \sqrt{4} + \sqrt{63} \\ \\ = \: \bf \: 2 + \sqrt{63}$

ANSWER:

$\huge\bold \implies \: 2 + \sqrt{63}$.