Verified answer

First of all, multiplying √(√2 + ³√3) by √(√2 + ³√3) yields (√2 + ³√3).

Next, we remove the square root by multiplying by (√2 - ³√3):

(√2 + ³√3) * (√2 - ³√3) = 2 + ³√9.

To remove the cube root, use difference of cubes x^3 - y^3 = (x - y)(x^2 + xy + y^2):

(2 + ³√9)(2^2 + 2 * ³√9 + (³√9)^2) = 2^3 - 9 = -1, which is rationalized.

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Overall rationalising factor:

√(√2 + ³√3)(√2 - ³√3)(4 + 2 * ³√9 + ³√81).

I hope this helps!