multiply and simplify by factoring

sqrt20a^11b*sqrt8a^12b^11

To multiply and simplify by factoring, we can use the property of radicals which states that √(a) * √(b) = √(ab).

Let's apply this property to the given expression:
√(20a^11b) * √(8a^12b^11)

First, let's identify the perfect square factors under the square roots:
√(20a^11b) can be written as √(4 * 5 * a^10 * a * b)
Similarly, √(8a^12b^11) can be written as √(4 * 2 * a^10 * a^2 * b^10 * b)

Now we can simplify the expression:
√(4 * 5 * a^10 * a * b) * √(4 * 2 * a^10 * a^2 * b^10 * b)
= 2 * √(5 * a^10 * a * b) * 2 * √(2 * a^10 * a^2 * b^10 * b)
= 4 * √(5 * 2 * a^10 * a * b^10 * a^2 * b)
= 4 * √(10 * a^13 * b^11)

Therefore, the simplified expression is:
4√(10a^13b^11)