Answer :
To solve the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex], we'll simplify each part of the expression and then find the equivalent choice.
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
[tex]\(\sqrt{32}\)[/tex] can be rewritten as [tex]\(\sqrt{16 \times 2}\)[/tex].
Using the property of square roots, [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex], we get:
[tex]\(\sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \times \sqrt{2}\)[/tex].
2. Rewrite the expression:
Now substitute back into the original expression:
[tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
3. Combine like terms:
Since both terms contain [tex]\(\sqrt{2}\)[/tex], we can factor [tex]\(\sqrt{2}\)[/tex] out:
[tex]\(4\sqrt{2} - \sqrt{2} = (4 - 1) \times \sqrt{2} = 3\sqrt{2}\)[/tex].
4. Determine the equivalent choice:
The simplified expression is [tex]\(3\sqrt{2}\)[/tex].
Therefore, the choice equivalent to the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] is:
B. [tex]\(3\sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
[tex]\(\sqrt{32}\)[/tex] can be rewritten as [tex]\(\sqrt{16 \times 2}\)[/tex].
Using the property of square roots, [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex], we get:
[tex]\(\sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \times \sqrt{2}\)[/tex].
2. Rewrite the expression:
Now substitute back into the original expression:
[tex]\(4\sqrt{2} - \sqrt{2}\)[/tex].
3. Combine like terms:
Since both terms contain [tex]\(\sqrt{2}\)[/tex], we can factor [tex]\(\sqrt{2}\)[/tex] out:
[tex]\(4\sqrt{2} - \sqrt{2} = (4 - 1) \times \sqrt{2} = 3\sqrt{2}\)[/tex].
4. Determine the equivalent choice:
The simplified expression is [tex]\(3\sqrt{2}\)[/tex].
Therefore, the choice equivalent to the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] is:
B. [tex]\(3\sqrt{2}\)[/tex].