To determine which expression simplifies to [tex]\(2 \sqrt{15}\)[/tex], let's first evaluate the numerical values of the given square roots:
A. [tex]\(\sqrt{17}\)[/tex] is approximately [tex]\(4.1231\)[/tex].
B. [tex]\(\sqrt{19}\)[/tex] is approximately [tex]\(4.3589\)[/tex].
C. [tex]\(\sqrt{30}\)[/tex] is approximately [tex]\(5.4772\)[/tex].
D. [tex]\(\sqrt{60}\)[/tex] is approximately [tex]\(7.7460\)[/tex].
Next, let's check if any of these expressions can be simplified to [tex]\(2 \sqrt{15}\)[/tex].
To see if [tex]\(\sqrt{60}\)[/tex] can be simplified, we notice:
[tex]\[
\sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2 \times \sqrt{15}
\][/tex]
Evaluating this simplification, we can clearly see that
[tex]\[
\sqrt{60} = 2 \sqrt{15}
\][/tex]
So indeed, among the given options, [tex]\(\sqrt{60}\)[/tex] simplifies to [tex]\(2 \sqrt{15}\)[/tex].
Thus, the correct answer is:
D. [tex]\(\sqrt{60}\)[/tex]
