Simplify. (2x square root of 2x)(3 square root of 5x)?

Question

Simplify.
1. (2x square root of 2x)(3 square root of 5x)

2. square root of 18 over square root of 2

3. Evaluate square root of -36, if possible

Answer 1

1. (2x sqrt(2x)) * (3 sqrt(5x))
= (2x) * (3) * (sqrt(2x))(sqrt(5x))
= (6x) * (sqrt(10x^2))
= 6x * abs(x) * sqrt(10)
= 6x*(x)* sqrt(10) if x >= 0 OR 6x*(-x)* sqrt(10) if x < 0
= 6x^2 sqrt(10) if x >= 0 OR -6x^2 sqrt(10) if x < 0

2. sqrt(18) / sqrt(2)
= sqrt(18/2)
= sqrt(9)
= sqrt(3^2)
=abs(3)
=3.

3. sqrt(-36)
= sqrt(6^2*(-1))
= abs(6) * sqrt(-1)
= 6 * sqrt(-1)
= 6i, where i = sqrt(-1).

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Some annotations:
[a]    abs(x) = absolute value of x.
[b]    abs(x) is defined by the following:
      abs(x) = x if x >= 0
      abs(x) = -x if x < 0.

For example, abs(5) = 5, abs(0) = 0 and abs(-4) = -(-4) = 4.

Answer 2

1) (2x√2x ) (3√5x) = 6x √2x √5x
= 6x √10x²
=± 6x² √10

2)√18 / √2 = √ 18/2
= √9 = ± 3

3) √-36 = ± 6i
i = √-1
i² = -1

Answer 3

1. 2x√(2x)3√(5x)=6x√(10x^2)=6x^2√10

2. √18/√2=√9=3

3. √-36=6i where i=√-1

Answer 4

1) 6x^2 sqr(2x*5x)
ans: 6x^3 sqr(10)

2) 3

3) it is imposible because you can't have a negative number under a squared root