To express [tex]\(\sqrt{3} \sqrt{6}\)[/tex] in its simplest radical form, let's follow these steps:
1. Multiply the square roots: Recall that the product of two square roots can be combined under a single square root:
[tex]\[
\sqrt{3} \cdot \sqrt{6} = \sqrt{3 \cdot 6}
\][/tex]
2. Perform the multiplication inside the square root: Multiply the numbers inside the square root:
[tex]\[
3 \cdot 6 = 18
\][/tex]
So, we have:
[tex]\[
\sqrt{3} \cdot \sqrt{6} = \sqrt{18}
\][/tex]
3. Simplify the square root: The number 18 can be factored into its prime factors:
[tex]\[
18 = 9 \cdot 2 = 3^2 \cdot 2
\][/tex]
4. Extract the square root of the perfect square: Recall that the square root of a product is the product of the square roots:
[tex]\[
\sqrt{18} = \sqrt{3^2 \cdot 2} = \sqrt{3^2} \cdot \sqrt{2}
\][/tex]
Since [tex]\(\sqrt{3^2} = 3\)[/tex], we get:
[tex]\[
\sqrt{18} = 3 \sqrt{2}
\][/tex]
Therefore, the simplest radical form of [tex]\(\sqrt{3} \sqrt{6}\)[/tex] is:
[tex]\[
3 \sqrt{2}
\][/tex]
So, the answer is:
[tex]\[
\boxed{3 \sqrt{2}}
\][/tex]
