To simplify the radical [tex]\(\sqrt{50}\)[/tex], we start by breaking down 50 into its prime factors.
The number 50 can be factored as [tex]\(50 = 25 \times 2\)[/tex]. Notice that 25 is a perfect square. We can then rewrite the square root of 50 using these factors:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2}
\][/tex]
Using the property of square roots that allows us to separate the factors, we have:
[tex]\[
\sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}
\][/tex]
Since [tex]\(\sqrt{25}\)[/tex] is 5 (because [tex]\(5^2 = 25\)[/tex]), we can simplify further:
[tex]\[
\sqrt{25} \times \sqrt{2} = 5 \sqrt{2}
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{50}\)[/tex] is:
[tex]\[
5 \sqrt{2}
\][/tex]
The correct answer from the given choices is:
D. [tex]\(5 \sqrt{2}\)[/tex]
For verification, converting [tex]\(5 \sqrt{2}\)[/tex] to a numerical form, we get approximately 7.0710678118654755. This confirms that our simplified radical form is correct.
