To solve the problem of adding [tex]\(\sqrt[3]{7} + \sqrt{7}\)[/tex], let's proceed step-by-step:
1. Calculate the cube root of 7 ([tex]\(\sqrt[3]{7}\)[/tex]):
The cube root of 7, denoted as [tex]\(\sqrt[3]{7}\)[/tex], is a number which, when multiplied by itself three times, equals 7.
[tex]\[
\sqrt[3]{7} \approx 1.913
\][/tex]
2. Calculate the square root of 7 ([tex]\(\sqrt{7}\)[/tex]):
The square root of 7, denoted as [tex]\(\sqrt{7}\)[/tex], is a number which, when multiplied by itself, equals 7.
[tex]\[
\sqrt{7} \approx 2.646
\][/tex]
3. Add the two values calculated:
Now, we add the two results:
[tex]\[
\sqrt[3]{7} + \sqrt{7} \approx 1.913 + 2.646 = 4.559
\][/tex]
Given the result:
4.559
None of the provided options (A) [tex]\(\sqrt[4]{7}\)[/tex], (B) [tex]\(\sqrt[3]{14}\)[/tex], (C) [tex]\(\sqrt[4]{14}\)[/tex], or (D) [tex]\(\sqrt[3]{49}\)[/tex] directly matches this numerical value. Therefore, it seems that none of the provided answers are correct based on this calculation.
Thus, the answer options do not match the calculated value of [tex]\(\sqrt[3]{7} + \sqrt{7}\)[/tex].
