Multiplying Radicals?

Question

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Number 1. 5 root 6 times 2x root 6.
Number 2: root 12 times root 3xy squared.
Number 3: 4 times root 3 times -5 times root 21.
Number 4: 5 times root 45 times x cubed times y squared times root 5x.
Number 5: root 24 plus root 54. NOTICE number 5 is an addition problem.

Answer 1

1) 5√6 × 2x√6 = 10x(√6)² = (10 × 6)x = 60x

2) √12 × √3xy² = √36xy² = 6xy² (assuming that only the 3 is under the root; can't tell from the way you posted)

3) 4√3 × -5√21 = -20√(3 × 21) = -20√(9 × 7) = -20√9√7 = -(20 × 3)√7 = -60√7

4) 5√45 × x³ × y² × x√5 = 5x⁴y²√(5 × 45) = 5x⁴y²√225 = (5 × 15)x⁴y² = 75x⁴y² (again, I'm assuming "root 5x" means x√5, not √(5x).)

5) √24 + √54 = √(4 × 6) + √(9 × 6) = √4√6 + √9√6 = 2√6 + 3√6 = 5√6

Answer 2

simplify as much as possible
get everything to a square root.
1. 5 root 6 times 2x root 6 is the same as the root of 31 times the root of 10.