Answer :
To solve the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] and find the equivalent choice, we need to simplify it:
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- First, break down 32 into its factors, focusing on perfect squares.
- [tex]\(32 = 16 \times 2\)[/tex].
- We can rewrite [tex]\(\sqrt{32}\)[/tex] as [tex]\(\sqrt{16 \times 2}\)[/tex].
- Since [tex]\(\sqrt{16}\)[/tex] is a perfect square, it simplifies to 4.
- Therefore, [tex]\(\sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \times \sqrt{2}\)[/tex].
2. Simplify the entire expression:
- Start with the expression: [tex]\(\sqrt{32} - \sqrt{2}\)[/tex].
- Substitute the simplified form of [tex]\(\sqrt{32}\)[/tex] into the expression:
[tex]\[ 4 \times \sqrt{2} - \sqrt{2} \][/tex]
3. Combine like terms:
- Both terms involve [tex]\(\sqrt{2}\)[/tex].
- Therefore, you can combine them:
[tex]\[ 4\sqrt{2} - 1\sqrt{2} = (4 - 1)\sqrt{2} = 3\sqrt{2} \][/tex]
The expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] simplifies to [tex]\(3\sqrt{2}\)[/tex].
Thus, the equivalent choice is C. [tex]\(3\sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- First, break down 32 into its factors, focusing on perfect squares.
- [tex]\(32 = 16 \times 2\)[/tex].
- We can rewrite [tex]\(\sqrt{32}\)[/tex] as [tex]\(\sqrt{16 \times 2}\)[/tex].
- Since [tex]\(\sqrt{16}\)[/tex] is a perfect square, it simplifies to 4.
- Therefore, [tex]\(\sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \times \sqrt{2}\)[/tex].
2. Simplify the entire expression:
- Start with the expression: [tex]\(\sqrt{32} - \sqrt{2}\)[/tex].
- Substitute the simplified form of [tex]\(\sqrt{32}\)[/tex] into the expression:
[tex]\[ 4 \times \sqrt{2} - \sqrt{2} \][/tex]
3. Combine like terms:
- Both terms involve [tex]\(\sqrt{2}\)[/tex].
- Therefore, you can combine them:
[tex]\[ 4\sqrt{2} - 1\sqrt{2} = (4 - 1)\sqrt{2} = 3\sqrt{2} \][/tex]
The expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] simplifies to [tex]\(3\sqrt{2}\)[/tex].
Thus, the equivalent choice is C. [tex]\(3\sqrt{2}\)[/tex].