Let's simplify the expression step by step.
Start with the expression: \((3\sqrt{8} + \sqrt{18}) \cdot 2\)
Simplify \(\sqrt{8}\) and \(\sqrt{18}\):
- \(\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}\)
- \(\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}\)
Substitute back into the expression: \[ 3\sqrt{8} + \sqrt{18} = 3(2\sqrt{2}) + 3\sqrt{2} \] \[ = 6\sqrt{2} + 3\sqrt{2} = 9\sqrt{2} \]
Now multiply by 2: \[ (3\sqrt{8} + \sqrt{18}) \cdot 2 = 9\sqrt{2} \cdot 2 = 18\sqrt{2} \]
Thus, the value of the expression \((3\sqrt{8} + \sqrt{18}) \cdot 2\) is \(18\sqrt{2}\).
