The product of 2√3 and 3√12 in simplified form is 6√36. To simplify this expression, we can first multiply 2 and 3 to get 6. Then, we can simplify the square root of 3 and the square root of 12 by finding their prime factorizations:
√3 = √(3 * 1) = √3
√12 = √(12 * 1) = √(2^2 * 3) = 2√3
So, 2√3 = 2 * √3 = 2 * √3
And, 3√12 = 3 * 2√3 = 6√3
Finally, the product of 2√3 and 3√12 is 6 * 6√3 = 6√36.