Answer :
To solve the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] and find which choice is equivalent, we need to simplify the expression:
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
- Factor 18 to find its prime factors: [tex]\(18 = 9 \times 2\)[/tex].
- Since 9 is a perfect square, you can simplify [tex]\(\sqrt{18}\)[/tex] as follows:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2}
\][/tex]
2. Substitute and simplify the expression:
- Replace [tex]\(\sqrt{18}\)[/tex] with [tex]\(3 \sqrt{2}\)[/tex] in the original expression:
[tex]\[
3 \sqrt{2} - \sqrt{2}
\][/tex]
3. Combine like terms:
- Both terms have [tex]\(\sqrt{2}\)[/tex] as a factor, so you can factor out [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
(3 - 1)\sqrt{2} = 2 \sqrt{2}
\][/tex]
4. Identify the equivalent choice:
- Comparing [tex]\(2 \sqrt{2}\)[/tex] with the provided options, we see that the correct equivalent choice is:
- B. [tex]\(2 \sqrt{2}\)[/tex]
Therefore, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2 \sqrt{2}\)[/tex], making the correct answer choice B.
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
- Factor 18 to find its prime factors: [tex]\(18 = 9 \times 2\)[/tex].
- Since 9 is a perfect square, you can simplify [tex]\(\sqrt{18}\)[/tex] as follows:
[tex]\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2}
\][/tex]
2. Substitute and simplify the expression:
- Replace [tex]\(\sqrt{18}\)[/tex] with [tex]\(3 \sqrt{2}\)[/tex] in the original expression:
[tex]\[
3 \sqrt{2} - \sqrt{2}
\][/tex]
3. Combine like terms:
- Both terms have [tex]\(\sqrt{2}\)[/tex] as a factor, so you can factor out [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
(3 - 1)\sqrt{2} = 2 \sqrt{2}
\][/tex]
4. Identify the equivalent choice:
- Comparing [tex]\(2 \sqrt{2}\)[/tex] with the provided options, we see that the correct equivalent choice is:
- B. [tex]\(2 \sqrt{2}\)[/tex]
Therefore, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2 \sqrt{2}\)[/tex], making the correct answer choice B.