Answer :
To solve the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] and find which choice is equivalent to it, let's go through the steps to simplify it:
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- Notice that [tex]\(\sqrt{50} = \sqrt{25 \times 2}\)[/tex].
- We can break this down as [tex]\(\sqrt{25} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{25} = 5\)[/tex], we have [tex]\(5\sqrt{2}\)[/tex].
2. Rewrite the original expression:
- The original expression is [tex]\(\sqrt{50} - \sqrt{2}\)[/tex].
- Substituting [tex]\(\sqrt{50}\)[/tex] with [tex]\(5\sqrt{2}\)[/tex], it becomes:
[tex]\[
5\sqrt{2} - \sqrt{2}
\][/tex]
3. Factor out [tex]\(\sqrt{2}\)[/tex]:
- Both terms have [tex]\(\sqrt{2}\)[/tex] in common, so we can factor it out:
[tex]\[
(5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
Thus, the expression simplifies to [tex]\(4\sqrt{2}\)[/tex], which matches choice A.
The equivalent choice for the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] is:
- A. [tex]\(4\sqrt{2}\)[/tex]
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- Notice that [tex]\(\sqrt{50} = \sqrt{25 \times 2}\)[/tex].
- We can break this down as [tex]\(\sqrt{25} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{25} = 5\)[/tex], we have [tex]\(5\sqrt{2}\)[/tex].
2. Rewrite the original expression:
- The original expression is [tex]\(\sqrt{50} - \sqrt{2}\)[/tex].
- Substituting [tex]\(\sqrt{50}\)[/tex] with [tex]\(5\sqrt{2}\)[/tex], it becomes:
[tex]\[
5\sqrt{2} - \sqrt{2}
\][/tex]
3. Factor out [tex]\(\sqrt{2}\)[/tex]:
- Both terms have [tex]\(\sqrt{2}\)[/tex] in common, so we can factor it out:
[tex]\[
(5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
Thus, the expression simplifies to [tex]\(4\sqrt{2}\)[/tex], which matches choice A.
The equivalent choice for the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] is:
- A. [tex]\(4\sqrt{2}\)[/tex]