Answer :



Simplifying 1st part by rationalizing the expression by multiplying and dividing by 2 + √2


 


=  = = 4√3 + 2√6


Simplifying 2nd part by rationalizing the expression by multiplying and dividing by 4√3 + √18



=   


Simplifying 3rd part by rationalizing the expression by multiplying and dividing by 3 + √12



= -


Putting all values we get;


4√3 + 2√6 – (4√3 – √18) + (3√2 + √24)


4√3 + √6 × 22 – (4√3 – √18) + (√2 × 32 + √24)


4√3 + √24 – (4√3 – √18) + (√18 + √24)


= 2√24 = 4√6

Hence,

  = 4√6

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