Sure, let's simplify the given expression [tex]\(\sqrt{50}\)[/tex].
Step 1: Factor 50 into its prime factors.
[tex]\[ 50 = 2 \times 25 \][/tex]
Step 2: Recognize that 25 is a perfect square.
[tex]\[ 25 = 5 \times 5 \][/tex]
Step 3: Rewrite the expression inside the square root.
[tex]\[ \sqrt{50} = \sqrt{2 \times 25} \][/tex]
Step 4: Use the property of square roots that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex].
[tex]\[ \sqrt{2 \times 25} = \sqrt{2} \times \sqrt{25} \][/tex]
Step 5: Simplify [tex]\(\sqrt{25}\)[/tex].
[tex]\[ \sqrt{25} = 5 \][/tex]
Step 6: Combine the results.
[tex]\[ \sqrt{2} \times 5 = 5 \sqrt{2} \][/tex]
Thus, the simplified form of [tex]\(\sqrt{50}\)[/tex] is [tex]\(5 \sqrt{2}\)[/tex].
The correct answer is:
C. [tex]\( 5 \sqrt{2} \)[/tex]
