Question

(3sqrt(2))/(sqrt(3) + sqrt(6)) + (4sqrt(3))/(sqrt(2) + sqrt(6)) + (sqrt(6))/(sqrt(2) + sqrt(3))​

Answer 1

0 is the answer

go to above pic

Answer 2

$\displaystyle \sf \frac{3 \sqrt{2} }{ \sqrt{3} + \sqrt{6} } + \frac{4 \sqrt{3} }{ \sqrt{2} + \sqrt{6} } + \frac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3} } = \bf 2( \sqrt{18} - \sqrt{6})$

Given :

The expression

$\displaystyle \sf \frac{3 \sqrt{2} }{ \sqrt{3} + \sqrt{6} } + \frac{4 \sqrt{3} }{ \sqrt{2} + \sqrt{6} } + \frac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3} }$

To find :

To simplify the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf \frac{3 \sqrt{2} }{ \sqrt{3} + \sqrt{6} } + \frac{4 \sqrt{3} }{ \sqrt{2} + \sqrt{6} } + \frac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3} }$

Step 2 of 2 :

Simplify the expression

$\displaystyle \sf \frac{3 \sqrt{2} }{ \sqrt{3} + \sqrt{6} } + \frac{4 \sqrt{3} }{ \sqrt{2} + \sqrt{6} } + \frac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3} }$

$\displaystyle \sf = \frac{3 \sqrt{2} (\sqrt{3} - \sqrt{6})}{ (\sqrt{3} + \sqrt{6}) (\sqrt{3} - \sqrt{6}) } + \frac{4 \sqrt{3} ( \sqrt{2} - \sqrt{6} )}{( \sqrt{2} + \sqrt{6} )( \sqrt{2} - \sqrt{6} ) } + \frac{ \sqrt{6} (\sqrt{2} - \sqrt{3} ) }{ (\sqrt{2} + \sqrt{3} ) (\sqrt{2} - \sqrt{3} )}$

$\displaystyle \sf = \frac{3 \sqrt{2} (\sqrt{3} - \sqrt{6})}{ {( \sqrt{3} )}^{2} - {( \sqrt{6} )}^{2} } + \frac{4 \sqrt{3} ( \sqrt{2} - \sqrt{6} )}{{( \sqrt{2} )}^{2} - {( \sqrt{6} )}^{2} } + \frac{ \sqrt{6} (\sqrt{2} - \sqrt{3} ) }{ {( \sqrt{2} )}^{2} - {( \sqrt{3} )}^{2}}$

$\displaystyle \sf = \frac{3 \sqrt{2} (\sqrt{3} - \sqrt{6})}{ 3 - 6 } + \frac{4 \sqrt{3} ( \sqrt{2} - \sqrt{6} )}{2 - 6 } + \frac{ \sqrt{6} (\sqrt{2} - \sqrt{3} ) }{2 - 3}$

$\displaystyle \sf = \frac{3 \sqrt{2} (\sqrt{3} - \sqrt{6})}{ - 3} + \frac{4 \sqrt{3} ( \sqrt{2} - \sqrt{6} )}{ - 4 } + \frac{ \sqrt{6} (\sqrt{2} - \sqrt{3} ) }{ - 1}$

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

$\displaystyle \sf = - \sqrt{6} + \sqrt{12} - \sqrt{6} + \sqrt{18} - \sqrt{12} + \sqrt{18}$

$\displaystyle \sf{ = 2( \sqrt{18} - \sqrt{6}) }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ the value of (√5+√2)²

https://brainly.in/question/3299659

2. Simplify ( 8+√5)(8-√5).

https://brainly.in/question/17061574