Answer :
To solve the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex], we'll start by simplifying each of the square roots.
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- Notice that 32 can be expressed as the product of 16 and 2:
[tex]\[
\sqrt{32} = \sqrt{16 \times 2}
\][/tex]
- We can simplify this by taking the square root of 16 (since 16 is a perfect square):
[tex]\[
\sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \times \sqrt{2}
\][/tex]
2. Rewrite the original expression:
With [tex]\(\sqrt{32}\)[/tex] simplified, our expression becomes:
[tex]\[
4\sqrt{2} - \sqrt{2}
\][/tex]
3. Subtract the square root terms:
Both terms contain [tex]\(\sqrt{2}\)[/tex]. We can factor out [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
(4\sqrt{2} - \sqrt{2}) = (4 - 1)\sqrt{2} = 3\sqrt{2}
\][/tex]
Therefore, the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] simplifies to [tex]\(3\sqrt{2}\)[/tex].
So, the correct answer is A. [tex]\(3 \sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{32}\)[/tex]:
- Notice that 32 can be expressed as the product of 16 and 2:
[tex]\[
\sqrt{32} = \sqrt{16 \times 2}
\][/tex]
- We can simplify this by taking the square root of 16 (since 16 is a perfect square):
[tex]\[
\sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \times \sqrt{2}
\][/tex]
2. Rewrite the original expression:
With [tex]\(\sqrt{32}\)[/tex] simplified, our expression becomes:
[tex]\[
4\sqrt{2} - \sqrt{2}
\][/tex]
3. Subtract the square root terms:
Both terms contain [tex]\(\sqrt{2}\)[/tex]. We can factor out [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
(4\sqrt{2} - \sqrt{2}) = (4 - 1)\sqrt{2} = 3\sqrt{2}
\][/tex]
Therefore, the expression [tex]\(\sqrt{32} - \sqrt{2}\)[/tex] simplifies to [tex]\(3\sqrt{2}\)[/tex].
So, the correct answer is A. [tex]\(3 \sqrt{2}\)[/tex].