Answer :
Let's solve the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- We can express 32 as a product: [tex]\(32 = 16 \times 2\)[/tex].
- This gives us [tex]\(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{16} = 4\)[/tex], we can simplify further: [tex]\(\sqrt{32} = 4\sqrt{2}\)[/tex].
2. Subtract [tex]\(\sqrt{2}\)[/tex] from [tex]\(4\sqrt{2}\)[/tex]:
- Our expression now is [tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
- Both terms have [tex]\(\sqrt{2}\)[/tex] in common, so we can combine them:
[tex]\((4 - 1)\sqrt{2} = 3\sqrt{2}\)[/tex].
3. Conclusion:
- The simplified form of the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] is [tex]\(3\sqrt{2}\)[/tex].
So, the equivalent choice is B. [tex]\(3 \sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- We can express 32 as a product: [tex]\(32 = 16 \times 2\)[/tex].
- This gives us [tex]\(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{16} = 4\)[/tex], we can simplify further: [tex]\(\sqrt{32} = 4\sqrt{2}\)[/tex].
2. Subtract [tex]\(\sqrt{2}\)[/tex] from [tex]\(4\sqrt{2}\)[/tex]:
- Our expression now is [tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
- Both terms have [tex]\(\sqrt{2}\)[/tex] in common, so we can combine them:
[tex]\((4 - 1)\sqrt{2} = 3\sqrt{2}\)[/tex].
3. Conclusion:
- The simplified form of the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] is [tex]\(3\sqrt{2}\)[/tex].
So, the equivalent choice is B. [tex]\(3 \sqrt{2}\)[/tex].