Answer :
To solve the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex], let's simplify it step by step.
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
We can break down the square root of 18 as follows:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
\][/tex]
2. Substitute back into the expression:
Now, replace [tex]\(\sqrt{18}\)[/tex] with [tex]\(3\sqrt{2}\)[/tex]:
[tex]\[
3\sqrt{2} - \sqrt{2}
\][/tex]
3. Combine like terms:
Since both terms are like terms ([tex]\(\sqrt{2}\)[/tex] is common), you can combine them:
[tex]\[
(3\sqrt{2} - 1\sqrt{2}) = 2\sqrt{2}
\][/tex]
Therefore, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex], making option C the correct choice.
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
We can break down the square root of 18 as follows:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
\][/tex]
2. Substitute back into the expression:
Now, replace [tex]\(\sqrt{18}\)[/tex] with [tex]\(3\sqrt{2}\)[/tex]:
[tex]\[
3\sqrt{2} - \sqrt{2}
\][/tex]
3. Combine like terms:
Since both terms are like terms ([tex]\(\sqrt{2}\)[/tex] is common), you can combine them:
[tex]\[
(3\sqrt{2} - 1\sqrt{2}) = 2\sqrt{2}
\][/tex]
Therefore, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex], making option C the correct choice.