To simplify [tex]\(\sqrt{32}\)[/tex]:
1. First, we express 32 as a product of its factors that include a perfect square. The number 32 can be factored into 16 and 2, since 32 = 16 × 2.
2. Using the property of square roots that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex], we rewrite [tex]\(\sqrt{32}\)[/tex] as:
[tex]\[
\sqrt{32} = \sqrt{16 \times 2}
\][/tex]
3. Next, we take the square root of 16 and the square root of 2 separately. The square root of 16 is 4, and the square root of 2 remains as [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
\sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \times \sqrt{2}
\][/tex]
Thus, the simplified form of [tex]\(\sqrt{32}\)[/tex] is [tex]\(4 \sqrt{2}\)[/tex].
Considering the problem's options, it is already simplified, so comparing it:
- [tex]\(\sqrt{32}\)[/tex] simplifies to [tex]\(4 \sqrt{2}\)[/tex], not 4 [tex]\(\sqrt{8}\)[/tex] and not 16 either.
So the correct simplified form of [tex]\(\sqrt{32}\)[/tex] is [tex]\(4 \sqrt{2}\)[/tex].
