√144 = 12 which is a positive integer. Thus one set it belongs to is N (natural numbers). It also belongs to Z (integers), Q (rational numbers), R (real numbers), and C (complex numbers) since N is a subset of all of these sets.

For the expressions:

1. Combine like terms

(11x² + 3x + 19) + (6x² - 18x - 8) = (11 + 6)x² + (3 - 18)x + (19 - 8)

= 17x² - 15x + 11.

2. Same idea as 1.

  (13x² + 6xy - 12y²) - (9x² - 4xy) = (13 - 9)x² + (6 - (-4))xy - 12y²

= 4x² + 10xy - 12y²

3. Use the distributive property a(b+c), and the law of exponents x^mxⁿ = x^m+n

-2xy(3xy³ - 5xy + 7y²) = -6x²y⁴ + 10x²y² - 14xy⁵

4. Use distributive property. Also apply property of square roots: √(xy) = (√x)(√y)

(11+√3)(4 - √11) = 11(4 - √11) + (√3)(4 - √11) = 44 - 11√11 + 4√3 - √33.