Question

Simplofy 3root2-2root3÷3root2+2root3+root12÷root3-root2

Answer 1

Hey here is your answer

Answer 2

Hello,


The number system is as follows :-

$\frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } + \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} }$
Since root 12 = 2 root 3


Now
Rationalizing the denominator :-

$\frac{ {(3 \sqrt{2} - 2 \sqrt{3} ) }^{2} }{ {(3 \sqrt{2} )}^{2} - ( {2 \sqrt{3} )}^{2} } + \frac{2 \sqrt{3} ( \sqrt{3} + \sqrt{2} )}{ { \sqrt{3} }^{2} - { \sqrt{2} }^{2} } \\ \\ = \frac{18 + 12 - 12 \sqrt{6} }{18 - 12} + \frac{6 + 2 \sqrt{6} }{3 - 2} \\ \\ = \frac{30 - 12 \sqrt{6} }{6} + 6 + 2 \sqrt{6} \\ \\ = \frac{6(5 - 2 \sqrt{6}) }{6} + 6 + 2 \sqrt{6} \\ \\ = 5 - 2 \sqrt{6} + 6 + 2 \sqrt{6} \\ \\ = 6 + 5 = 11$

Hence the answer is 11


So ,simplified .


Hope this will be helping you.......