To find the simplest form of [tex]\(\sqrt{125}\)[/tex], we need to simplify the square root expression.
Step 1: Factorize the number inside the square root.
[tex]\[ 125 = 5 \times 25 \][/tex]
Step 2: Recall that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]. Thus, we can write:
[tex]\[ \sqrt{125} = \sqrt{5 \times 25} \][/tex]
Step 3: Simplify the square root expression by separating it into its factors:
[tex]\[ \sqrt{125} = \sqrt{5} \times \sqrt{25} \][/tex]
Step 4: Evaluate the square root of 25:
[tex]\[ \sqrt{25} = 5 \][/tex]
Step 5: Substitute the evaluated square root back into the expression:
[tex]\[ \sqrt{125} = \sqrt{5} \times 5 = 5 \sqrt{5} \][/tex]
Thus, the simplest form of [tex]\(\sqrt{125}\)[/tex] is [tex]\(5 \sqrt{5}\)[/tex].
Therefore, the correct answer is:
A. [tex]\(5 \sqrt{5}\)[/tex]
