Answer :
Let's simplify the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
The number 50 can be factored into [tex]\(25 \times 2\)[/tex], which allows us to rewrite the square root as:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
\][/tex]
2. Rewrite the expression:
Now that we have simplified [tex]\(\sqrt{50}\)[/tex] as [tex]\(5\sqrt{2}\)[/tex], the expression becomes:
[tex]\[
5\sqrt{2} - \sqrt{2}
\][/tex]
3. Factor out [tex]\(\sqrt{2}\)[/tex]:
Both terms have a common factor of [tex]\(\sqrt{2}\)[/tex]. We can factor [tex]\(\sqrt{2}\)[/tex] out:
[tex]\[
5\sqrt{2} - \sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
The expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] is equivalent to [tex]\(4\sqrt{2}\)[/tex].
So, the correct choice is D. [tex]\(4\sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
The number 50 can be factored into [tex]\(25 \times 2\)[/tex], which allows us to rewrite the square root as:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
\][/tex]
2. Rewrite the expression:
Now that we have simplified [tex]\(\sqrt{50}\)[/tex] as [tex]\(5\sqrt{2}\)[/tex], the expression becomes:
[tex]\[
5\sqrt{2} - \sqrt{2}
\][/tex]
3. Factor out [tex]\(\sqrt{2}\)[/tex]:
Both terms have a common factor of [tex]\(\sqrt{2}\)[/tex]. We can factor [tex]\(\sqrt{2}\)[/tex] out:
[tex]\[
5\sqrt{2} - \sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
The expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] is equivalent to [tex]\(4\sqrt{2}\)[/tex].
So, the correct choice is D. [tex]\(4\sqrt{2}\)[/tex].