To simplify [tex]\(\sqrt{75}\)[/tex], follow these steps:
1. Factor the number inside the square root:
- Break down [tex]\(75\)[/tex] into its prime factorization.
- [tex]\(75\)[/tex] can be factored into [tex]\(25 \times 3\)[/tex].
2. Simplify the square root:
- Recognize that [tex]\(25\)[/tex] is a perfect square.
- The square root of [tex]\(25\)[/tex] is [tex]\(5\)[/tex].
3. Express the original square root in simplified form:
- [tex]\(\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3}\)[/tex]
- Substitute the square root of [tex]\(25\)[/tex] with [tex]\(5\)[/tex].
- This gives us [tex]\(5 \sqrt{3}\)[/tex].
Therefore, the simplified form of [tex]\(\sqrt{75}\)[/tex] is [tex]\(5 \sqrt{3}\)[/tex].
Thus, the correct answer is:
D. [tex]\(5 \sqrt{3}\)[/tex]
