The question is: Simplify (4a^(3/2)) * (2a^1\2))

The answer the book gives is: 8a^2

My work includes:

1. (4a^(3/2)) * (2a^1\2))

2. (sqrt(4)^3) * (sqrt(a)^3) * sqrt(2) * sqrt(a)

3. (sqrt(4)^3) * (sqrt(a)^4 * sqrt(2)

4. 2^3 * a^2 * sqrt(2)

Thus: 8a^2 * sqrt(2)

Is the book wrong, or how do I get rid of that sqrt(2)?

Thanks