Answer :
We start with the expression:
[tex]$$
\sqrt{50} - \sqrt{2}.
$$[/tex]
Step 1. Recognize that the number 50 can be factored as [tex]$25 \times 2$[/tex]. Using the property of square roots, we have:
[tex]$$
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}.
$$[/tex]
Step 2. Substitute the simplified form back into the original expression:
[tex]$$
\sqrt{50} - \sqrt{2} = 5\sqrt{2} - \sqrt{2}.
$$[/tex]
Step 3. Factor out the common term [tex]$\sqrt{2}$[/tex]:
[tex]$$
5\sqrt{2} - \sqrt{2} = (5-1)\sqrt{2} = 4\sqrt{2}.
$$[/tex]
Thus, the expression [tex]$\sqrt{50} - \sqrt{2}$[/tex] is equivalent to
[tex]$$
4\sqrt{2}.
$$[/tex]
This corresponds to the choice labeled as [tex]$4\sqrt{2}$[/tex].
[tex]$$
\sqrt{50} - \sqrt{2}.
$$[/tex]
Step 1. Recognize that the number 50 can be factored as [tex]$25 \times 2$[/tex]. Using the property of square roots, we have:
[tex]$$
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}.
$$[/tex]
Step 2. Substitute the simplified form back into the original expression:
[tex]$$
\sqrt{50} - \sqrt{2} = 5\sqrt{2} - \sqrt{2}.
$$[/tex]
Step 3. Factor out the common term [tex]$\sqrt{2}$[/tex]:
[tex]$$
5\sqrt{2} - \sqrt{2} = (5-1)\sqrt{2} = 4\sqrt{2}.
$$[/tex]
Thus, the expression [tex]$\sqrt{50} - \sqrt{2}$[/tex] is equivalent to
[tex]$$
4\sqrt{2}.
$$[/tex]
This corresponds to the choice labeled as [tex]$4\sqrt{2}$[/tex].