Answer :
To solve the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex], we can start by simplifying [tex]\(\sqrt{32}\)[/tex].
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- Notice that 32 can be expressed as [tex]\(16 \times 2\)[/tex]. Therefore, [tex]\(\sqrt{32} = \sqrt{16 \times 2}\)[/tex].
- We can split the square root into two parts: [tex]\(\sqrt{16} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{16} = 4\)[/tex], it simplifies to [tex]\(4\sqrt{2}\)[/tex].
2. Substitute the simplified value:
- Replace [tex]\(\sqrt{32}\)[/tex] with [tex]\(4\sqrt{2}\)[/tex] in the expression: [tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
3. Simplify the expression further:
- Factor out [tex]\(\sqrt{2}\)[/tex]: [tex]\((4 - 1)\sqrt{2}\)[/tex].
- This simplifies to [tex]\(3\sqrt{2}\)[/tex].
Therefore, the equivalent choice for the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] is [tex]\(3\sqrt{2}\)[/tex], which corresponds to option B.
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- Notice that 32 can be expressed as [tex]\(16 \times 2\)[/tex]. Therefore, [tex]\(\sqrt{32} = \sqrt{16 \times 2}\)[/tex].
- We can split the square root into two parts: [tex]\(\sqrt{16} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{16} = 4\)[/tex], it simplifies to [tex]\(4\sqrt{2}\)[/tex].
2. Substitute the simplified value:
- Replace [tex]\(\sqrt{32}\)[/tex] with [tex]\(4\sqrt{2}\)[/tex] in the expression: [tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
3. Simplify the expression further:
- Factor out [tex]\(\sqrt{2}\)[/tex]: [tex]\((4 - 1)\sqrt{2}\)[/tex].
- This simplifies to [tex]\(3\sqrt{2}\)[/tex].
Therefore, the equivalent choice for the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] is [tex]\(3\sqrt{2}\)[/tex], which corresponds to option B.