To find the sum of [tex]\( \sqrt[3]{7} + \sqrt{7} \)[/tex], we need to separately compute each term and then add them together.
1. Compute the cube root of 7, [tex]\( \sqrt[3]{7} \)[/tex]:
The value of [tex]\( \sqrt[3]{7} \)[/tex] is approximately [tex]\( 1.912931182772389 \)[/tex].
2. Compute the square root of 7, [tex]\( \sqrt{7} \)[/tex]:
The value of [tex]\( \sqrt{7} \)[/tex] is approximately [tex]\( 2.6457513110645907 \)[/tex].
3. Add these two results:
[tex]\[
\sqrt[3]{7} + \sqrt{7} \approx 1.912931182772389 + 2.6457513110645907
\][/tex]
Summing these values, we get:
[tex]\[
\sqrt[3]{7} + \sqrt{7} \approx 4.558682493836979
\][/tex]
Therefore, the sum [tex]\( \sqrt[3]{7} + \sqrt{7} \)[/tex] is approximately [tex]\( 4.558682493836979 \)[/tex].
