Question

guys solve it ...............​

Answer 1

Answer:

3×2=6

6×3=18

4×3=12

6×2=12

2×3=6

2×6=12 is the answer

Answer 2

Answer:

$\huge \fbox \purple { The Answer is 0 }$

Step-by-step explanation:

There are three terms

Let's solve each term one by one.

What we need to do is to just rationalise all the 3 terms.

$1st \: term \: = \frac{3 \sqrt{2} }{ (\sqrt{6} - \sqrt{3}) } \\ \\ = > \frac{3 \sqrt{2} \times ( \sqrt{6} + \sqrt{3} )}{( \sqrt{6} - \sqrt{3}) \times ( \sqrt{6} + \sqrt{3}) } \\ \\ = > \frac{3 \sqrt{12} + 3 \sqrt{6} }{6 - 3} \\ \\ = > \frac{3 \sqrt{2 \times 2 \times 3} + 3 \sqrt{2 \times 3} }{3} \\ \\ = > \frac{6 \sqrt{3} + 3 \sqrt{6} }{3} \\ \\ = > \frac{3(2 \sqrt{3} + \sqrt{6}) }{3} \\ \\ = > 2 \sqrt{3} + \sqrt{6}$

Now let's solve the second term :-

$2nd \: term \: = > \frac{4 \sqrt{3} }{ \sqrt{6} - \sqrt{2} } \\ \\ = > \frac{4 \sqrt{3} \times ( \sqrt{6} + \sqrt{2} ) }{( \sqrt{6} - \sqrt{2} ) \times ( \sqrt{6} + \sqrt{2} )} \\ \\ = > \frac{4 \sqrt{18} + 4 \sqrt{6} }{6 - 2} \\ \\ = > \frac{4 \sqrt{2 \times 3 \times 3} + 4 \sqrt{2 \times 3} }{4} \\ \\ = > \frac{12 \sqrt{2} + 4 \sqrt{6} }{4} \\ \\ = > \frac{4(3 \sqrt{2} + \sqrt{6} )}{4} \\ \\ = > 3 \sqrt{2} + \sqrt{6}$

Now let's solve the 3 rd term :-

$3rd \: term \: = > \frac{2 \sqrt{3} }{2 + \sqrt{6} } \\ \\ = > \frac{2 \sqrt{3} \times (2 - \sqrt{6}) }{(2 + \sqrt{6}) \times (2 - \sqrt{6} ) } \\ \\ = > \frac{4 \sqrt{3} - 2 \sqrt{18} }{4 - 6} \\ \\ = > \frac{4 \sqrt{3} - 2 \sqrt{2 \times 3 \times 3} }{ - 2} \\ \\ = > \frac{4 \sqrt{3} - 6 \sqrt{2} }{ - 2} \\ \\ = > \frac{2(2 \sqrt{3} - 3 \sqrt{2} ) }{ - 2} \\ \\ = > \frac{(2 \sqrt{3} - 3 \sqrt{2} )}{ - 1} \\ \\ = > - 2 \sqrt{3} + 3 \sqrt{2}$

Now let's put all the three solved term as given in question:-

Therefore:-

$\frac{3 \sqrt{2} }{ \sqrt{6} - \sqrt{3} } - \frac{4 \sqrt{3} }{ \sqrt{6} - \sqrt{2} } + \frac{2 \sqrt{3} }{2 + \sqrt{6} } \\ \\ now \: put \: the \: above \: solved \: values \\ \\ = > 2 \sqrt{3} + \sqrt{6} - (3 \sqrt{2} + \sqrt{6} ) + ( - 2 \sqrt{3} + 3 \sqrt{2} ) \\ \\ = > 2 \sqrt{3} + \sqrt{6} - 3 \sqrt{2} - \sqrt{6} - 2 \sqrt{3} + 3 \sqrt{2} \\ \\ = > 2 \sqrt{3} - 2 \sqrt{3} + \sqrt{6} - \sqrt{6} - 3 \sqrt{2} + 3 \sqrt{2} \\ \\ = > 0 + 0 + 0 \\ = > 0 \: answer$

$\huge \fbox \red {Hence the answer is 0 }$