Question

use the properties of radicals to simplify the expression.
\sqrt{2} \cdot \sqrt{72} = \square

Explanation:

Step1: Apply radical multiplication property

The property of radicals states that $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ for $a\geq0$ and $b\geq0$. So, we can combine the two square roots: $\sqrt{2} \cdot \sqrt{72}=\sqrt{2\times72}$.

Step2: Calculate the product inside the radical

Calculate $2\times72 = 144$. So now we have $\sqrt{144}$.

Step3: Simplify the square root

The square root of 144 is 12, since $12\times12 = 144$.

Answer:

12