Help with Multiplying Radicals?

Question

11: sqrt 33a^11b^11 times sqrt 3

12: k sqrt 2 times k sqrt 3

13: 3(sqrt 2+ sqrt 6)

14: 4(2 sqrt 2+3 sqrt 2

15: sqrt 2(3 sqrt 2-5 sqrt 2)

Answer 1

11: sqrt 33a^11b^11 times sqrt 3

= sqrt(33)a^11b^11*sqrt(3)

= sqrt(99)a^11b^11

12: k sqrt 2 times k sqrt 3

= ksqrt(2)*ksqrt(3)

= k^2sqrt(6)

13: 3(sqrt 2+ sqrt 6)

= 3(sqrt(2) + sqrt(6))

= 3(sqrt(2) + sqrt(2)sqrt(3))

= 3sqrt(2)(1 + sqrt(3))

14: 4(2 sqrt 2+3 sqrt 2)

= 4(2sqrt(2) + 3sqrt(2))

= 4(5sqrt(2))

= 20sqrt(2)

15: sqrt 2(3 sqrt 2-5 sqrt 2)

= sqrt(2)(3sqrt(2) - 5sqrt(2))

= sqrt(2)(-2sqrt(2))

= -2*2

= -4