To find the simplest form of [tex]\(\sqrt{200}\)[/tex], we start by simplifying the radical expression.
First, we express 200 as a product of its prime factors:
[tex]\[ 200 = 2 \times 100. \][/tex]
Next, break down 100 into its prime factors:
[tex]\[ 100 = 10^2. \][/tex]
Therefore:
[tex]\[ 200 = 2 \times 10^2. \][/tex]
We can now use the property of square roots [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex] to simplify [tex]\(\sqrt{200}\)[/tex]:
[tex]\[ \sqrt{200} = \sqrt{2 \times 10^2} = \sqrt{2} \times \sqrt{10^2}. \][/tex]
Since the square root of [tex]\(10^2\)[/tex] is simply 10:
[tex]\[ \sqrt{200} = \sqrt{2} \times 10 = 10\sqrt{2}. \][/tex]
Thus, [tex]\(\sqrt{200}\)[/tex] in its simplest form is:
[tex]\[ 10 \sqrt{2}. \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B.} \][/tex]
