Simplify.

Remove all perfect squares from inside the square root.

square root 112a^6

4a^3sqrt{7}

4√7*a^3

Step-by-step explanation:

a^6 is the same as (a^3) ^2. If we take the square root of this latter expression, the result will be a^3.

112 can be factored as follows: 2 * 56

2 * 7 * 8

2 * 7 * 2 * 4, or 7 4^2

Taking the square root of this last result yields 4√7.

Thus, √ (112a^6) = 4√7*a^3