To determine the value of [tex]\( \left(1^3 + 2^3 + 3^3 \right)^{1/2} \)[/tex], let's outline the steps involved in the calculation:
1. Calculate the cubes:
- [tex]\(1^3 = 1 \)[/tex]
- [tex]\(2^3 = 8 \)[/tex]
- [tex]\(3^3 = 27 \)[/tex]
2. Sum the cubes:
- [tex]\(1^3 + 2^3 + 3^3 = 1 + 8 + 27 = 36 \)[/tex]
3. Take the square root of the sum:
- [tex]\(\left(1^3 + 2^3 + 3^3\right)^{1/2} = 36^{1/2} \)[/tex]
- The square root of 36 is [tex]\(6\)[/tex].
Therefore, the final answer to the expression [tex]\( \left(1^3 + 2^3 + 3^3 \right)^{1/2} \)[/tex] is:
[tex]\[ \boxed{6.0} \][/tex]
