Let's simplify the given expression step-by-step:
Step 1: Write down the expression:
[tex]\[
\sqrt{32}
\][/tex]
Step 2: Break 32 into its prime factors:
[tex]\[
32 = 16 \times 2 = 4^2 \times 2
\][/tex]
Step 3: Use the property of square roots to separate the expression:
[tex]\[
\sqrt{32} = \sqrt{16 \times 2}
\][/tex]
Step 4: Simplify by taking the square root of 16:
[tex]\[
\sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2}
\][/tex]
Step 5: Calculate the square root of 16:
[tex]\[
\sqrt{16} = 4
\][/tex]
Step 6: Combine the simplified parts:
[tex]\[
\sqrt{32} = 4 \times \sqrt{2} = 4\sqrt{2}
\][/tex]
Upon completing these steps, we find that the simplified form of [tex]\(\sqrt{32}\)[/tex] is:
[tex]\[
4\sqrt{2}
\][/tex]
Thus, the correct answer is
[tex]\[
4\sqrt{2}
\][/tex]
