Answer :
To simplify the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex], let's break it down step by step:
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- We first express 32 as a product of its factors: [tex]\(32 = 16 \times 2\)[/tex].
- The square root of 32 can be rewritten using these factors: [tex]\(\sqrt{32} = \sqrt{16 \times 2}\)[/tex].
- We know [tex]\(\sqrt{16}\)[/tex] is 4, so [tex]\(\sqrt{32} = 4\sqrt{2}\)[/tex].
2. Subtract [tex]\(\sqrt{2}\)[/tex]:
- Now, substitute this back into the expression: [tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
- Since both terms have [tex]\(\sqrt{2}\)[/tex] as a common factor, we can factor it out: [tex]\(4\sqrt{2} - 1\sqrt{2} = (4 - 1)\sqrt{2} = 3\sqrt{2}\)[/tex].
3. Conclusion:
- The expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] simplifies to [tex]\(3\sqrt{2}\)[/tex].
Thus, the choice that is equivalent to the expression is [tex]\(\boxed{A. \, 3\sqrt{2}}\)[/tex].
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- We first express 32 as a product of its factors: [tex]\(32 = 16 \times 2\)[/tex].
- The square root of 32 can be rewritten using these factors: [tex]\(\sqrt{32} = \sqrt{16 \times 2}\)[/tex].
- We know [tex]\(\sqrt{16}\)[/tex] is 4, so [tex]\(\sqrt{32} = 4\sqrt{2}\)[/tex].
2. Subtract [tex]\(\sqrt{2}\)[/tex]:
- Now, substitute this back into the expression: [tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
- Since both terms have [tex]\(\sqrt{2}\)[/tex] as a common factor, we can factor it out: [tex]\(4\sqrt{2} - 1\sqrt{2} = (4 - 1)\sqrt{2} = 3\sqrt{2}\)[/tex].
3. Conclusion:
- The expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] simplifies to [tex]\(3\sqrt{2}\)[/tex].
Thus, the choice that is equivalent to the expression is [tex]\(\boxed{A. \, 3\sqrt{2}}\)[/tex].