Answer :

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

= = = 4√3 + 2√6

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

=

Simplifying 3^{rd} 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 × 2^{2} – (4√3 – √18) + (√2 × 3^{2} + √24)

4√3 + √24 – (4√3 – √18) + (√18 + √24)

= 2√24 = 4√6

Hence,= 4√6

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