High School

Which choice is equivalent to the expression below?

[tex]\sqrt{18}-\sqrt{2}[/tex]

A. [tex]\sqrt{16}[/tex]

B. [tex]16 \sqrt{2}[/tex]

C. [tex]2 \sqrt{2}[/tex]

D. 3

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.