Simplify the expression. (Assume that all variables are positive.) \[ \sqrt{245 k^{3}} \]

To simplify the expression \(\sqrt{245 k^{3}}\), we start by breaking it down. The number 245 can be factored: \[ 245 = 5 \times 49 = 5 \times 7^2 \] Now we rewrite the square root: \[ \sqrt{245 k^{3}} = \sqrt{5 \times 7^2 \times k^3} \] Applying the property of square roots that allows us to separate the terms, we get: \[ \sqrt{5} \times \sqrt{7^2} \times \sqrt{k^3} \] We know that \(\sqrt{7^2} = 7\) and we can simplify \(\sqrt{k^3}\) as follows: \[ \sqrt{k^3} = \sqrt{k^2 \times k} = \sqrt{k^2} \times \sqrt{k} = k \sqrt{k} \] Putting it all together, the expression simplifies to: \[ 7k \sqrt{k} \times \sqrt{5} = 7k \sqrt{5k} \] Therefore, the simplified expression is: \[ 7k \sqrt{5k} \]