Answer :
Let's simplify the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] step-by-step to find which choice is equivalent.
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
[tex]\(\sqrt{18}\)[/tex] can be rewritten by factoring 18. We know that 18 is [tex]\(9 \times 2\)[/tex], so:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2}
\][/tex]
We can break down the square root:
[tex]\[
\sqrt{18} = \sqrt{9} \times \sqrt{2}
\][/tex]
Since [tex]\(\sqrt{9} = 3\)[/tex], we have:
[tex]\[
\sqrt{18} = 3 \times \sqrt{2}
\][/tex]
2. Subtract [tex]\(\sqrt{2}\)[/tex]:
Now, substitute the simplified form of [tex]\(\sqrt{18}\)[/tex] into the expression:
[tex]\[
3\sqrt{2} - \sqrt{2}
\][/tex]
We can factor out [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
(3 - 1)\sqrt{2} = 2\sqrt{2}
\][/tex]
So, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex].
Therefore, the choice equivalent to the expression is:
C. [tex]\(2\sqrt{2}\)[/tex]
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
[tex]\(\sqrt{18}\)[/tex] can be rewritten by factoring 18. We know that 18 is [tex]\(9 \times 2\)[/tex], so:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2}
\][/tex]
We can break down the square root:
[tex]\[
\sqrt{18} = \sqrt{9} \times \sqrt{2}
\][/tex]
Since [tex]\(\sqrt{9} = 3\)[/tex], we have:
[tex]\[
\sqrt{18} = 3 \times \sqrt{2}
\][/tex]
2. Subtract [tex]\(\sqrt{2}\)[/tex]:
Now, substitute the simplified form of [tex]\(\sqrt{18}\)[/tex] into the expression:
[tex]\[
3\sqrt{2} - \sqrt{2}
\][/tex]
We can factor out [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
(3 - 1)\sqrt{2} = 2\sqrt{2}
\][/tex]
So, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex].
Therefore, the choice equivalent to the expression is:
C. [tex]\(2\sqrt{2}\)[/tex]