Questions: Perform the indicated operation. Simplify the answer when possible. sqrt(2) * sqrt(22) sqrt(2) * sqrt(22)= (Type an exact answer, using radicals as needed.)

Solution Steps

To solve the given problem, we need to use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). We will then simplify the resulting expression if possible.

We start with the expression \(\sqrt{2} \cdot \sqrt{22}\). Using the property of square roots, we can combine them under a single square root: \[ \sqrt{2} \cdot \sqrt{22} = \sqrt{2 \cdot 22} \]

Next, we calculate the product inside the square root: \[ 2 \cdot 22 = 44 \] So, the expression becomes: \[ \sqrt{2 \cdot 22} = \sqrt{44} \]

Finally, we calculate the square root of 44. The square root of 44 is approximately: \[ \sqrt{44} \approx 6.633 \]

Final Answer