Answer :
To solve the problem, we need to simplify the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] and find the equivalent choice among the given options.
1. Simplifying [tex]\(\sqrt{32}\)[/tex]:
- Begin by factoring 32: [tex]\(32 = 2^5\)[/tex].
- Apply the square root: [tex]\(\sqrt{32} = \sqrt{2^5} = \sqrt{(2^4 \times 2)}\)[/tex].
- Simplify further: [tex]\(\sqrt{(2^4 \times 2)} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{16} = 4\)[/tex], we get [tex]\(\sqrt{32} = 4\sqrt{2}\)[/tex].
2. Subtracting [tex]\(\sqrt{2}\)[/tex]:
- We have [tex]\(\sqrt{32} - \sqrt{2} = 4\sqrt{2} - \sqrt{2}\)[/tex].
- Factor out [tex]\(\sqrt{2}\)[/tex]: [tex]\((4 - 1)\sqrt{2} = 3\sqrt{2}\)[/tex].
3. Conclusion:
- The expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] simplifies to [tex]\(3\sqrt{2}\)[/tex].
Therefore, the correct answer is C. [tex]\(3\sqrt{2}\)[/tex].
1. Simplifying [tex]\(\sqrt{32}\)[/tex]:
- Begin by factoring 32: [tex]\(32 = 2^5\)[/tex].
- Apply the square root: [tex]\(\sqrt{32} = \sqrt{2^5} = \sqrt{(2^4 \times 2)}\)[/tex].
- Simplify further: [tex]\(\sqrt{(2^4 \times 2)} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{16} = 4\)[/tex], we get [tex]\(\sqrt{32} = 4\sqrt{2}\)[/tex].
2. Subtracting [tex]\(\sqrt{2}\)[/tex]:
- We have [tex]\(\sqrt{32} - \sqrt{2} = 4\sqrt{2} - \sqrt{2}\)[/tex].
- Factor out [tex]\(\sqrt{2}\)[/tex]: [tex]\((4 - 1)\sqrt{2} = 3\sqrt{2}\)[/tex].
3. Conclusion:
- The expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] simplifies to [tex]\(3\sqrt{2}\)[/tex].
Therefore, the correct answer is C. [tex]\(3\sqrt{2}\)[/tex].