Answer :
To solve the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex], let's simplify it step by step.
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
Notice that 18 can be factored into [tex]\(9 \times 2\)[/tex]. Therefore, we can write:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}
\][/tex]
Since [tex]\(\sqrt{9} = 3\)[/tex], we have:
[tex]\[
\sqrt{18} = 3\sqrt{2}
\][/tex]
2. Substitute and simplify the original expression:
The expression is [tex]\(\sqrt{18} - \sqrt{2}\)[/tex]. We substitute the simplified form of [tex]\(\sqrt{18}\)[/tex]:
[tex]\[
3\sqrt{2} - \sqrt{2}
\][/tex]
3. Combine like terms:
Both terms contain [tex]\(\sqrt{2}\)[/tex], so we can combine them:
[tex]\[
3\sqrt{2} - 1\sqrt{2} = (3 - 1)\sqrt{2} = 2\sqrt{2}
\][/tex]
Therefore, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex].
From the given choices, the equivalent expression is:
C. [tex]\(2\sqrt{2}\)[/tex]
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
Notice that 18 can be factored into [tex]\(9 \times 2\)[/tex]. Therefore, we can write:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}
\][/tex]
Since [tex]\(\sqrt{9} = 3\)[/tex], we have:
[tex]\[
\sqrt{18} = 3\sqrt{2}
\][/tex]
2. Substitute and simplify the original expression:
The expression is [tex]\(\sqrt{18} - \sqrt{2}\)[/tex]. We substitute the simplified form of [tex]\(\sqrt{18}\)[/tex]:
[tex]\[
3\sqrt{2} - \sqrt{2}
\][/tex]
3. Combine like terms:
Both terms contain [tex]\(\sqrt{2}\)[/tex], so we can combine them:
[tex]\[
3\sqrt{2} - 1\sqrt{2} = (3 - 1)\sqrt{2} = 2\sqrt{2}
\][/tex]
Therefore, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex].
From the given choices, the equivalent expression is:
C. [tex]\(2\sqrt{2}\)[/tex]