Question

multiply the radicals below. ensure your final answer is as simplified as possible:
$2\sqrt{6} \cdot 6\sqrt{7} = $

Explanation:

Step1: Multiply coefficients and radicals separately

Multiply the coefficients (2 and 6) and the radicals ($\sqrt{6}$ and $\sqrt{7}$) separately. The coefficient multiplication: $2\times6 = 12$. The radical multiplication: $\sqrt{6}\times\sqrt{7}=\sqrt{6\times7}=\sqrt{42}$ (using the property $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ for $a\geq0,b\geq0$).

Step2: Combine the results

Combine the coefficient and the radical: $12\times\sqrt{42}=12\sqrt{42}$.

Answer:

$12\sqrt{42}$