Questions: sqrt(22) * sqrt(2) = □ (Type an exact answer, using radicals as needed.)

Solution Steps

To multiply and simplify the expression \(\sqrt{22} \cdot \sqrt{2}\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). Therefore, we multiply the numbers inside the square roots and then simplify the resulting square root if possible.

We start with the expression: \[ \sqrt{22} \cdot \sqrt{2} \] Using the property of square roots, we can combine the two square roots: \[ \sqrt{22} \cdot \sqrt{2} = \sqrt{22 \cdot 2} \]

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

Now, we simplify \(\sqrt{44}\). We can factor \(44\) as: \[ 44 = 4 \cdot 11 \] Therefore, we can simplify: \[ \sqrt{44} = \sqrt{4 \cdot 11} = \sqrt{4} \cdot \sqrt{11} = 2\sqrt{11} \]

Final Answer