To simplify [tex]\(\sqrt{50}\)[/tex], follow these steps:
1. Identify factors of 50: Recognize that [tex]\(50\)[/tex] can be broken down into the product of [tex]\(25\)[/tex] and [tex]\(2\)[/tex] (since [tex]\(50 = 25 \times 2\)[/tex]).
2. Use the property of square roots: Recall that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]. Applying this property, decompose [tex]\(\sqrt{50}\)[/tex] as follows:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2}
\][/tex]
3. Simplify the square root: Since [tex]\(25\)[/tex] is a perfect square, we know that [tex]\(\sqrt{25} = 5\)[/tex]. Substituting this value into the equation, we get:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \times \sqrt{2}
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{50}\)[/tex] is:
[tex]\[
5 \sqrt{2}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{5 \sqrt{2}}
\][/tex]
