To determine which student found the correct cube root of 216, let's analyze each student's method one by one.
### Hadley's Method
Hadley claims the cube root of 216 is 72 because:
[tex]\[ 216 \div 3 = 72 \][/tex]
However, dividing 216 by 3 does not give us the cube root of 216. The cube root of a number [tex]\(x\)[/tex] is a number [tex]\(y\)[/tex] such that [tex]\(y^3 = x\)[/tex]. To check if 72 is the cube root of 216, we would have to verify if:
[tex]\[ 72^3 = 216 \][/tex]
Clearly, [tex]\(72^3\)[/tex] yields a number much larger than 216. Thus, Hadley's method and result of 72 are incorrect.
### Florence's Method
Florence claims the cube root of 216 is 648 because:
[tex]\[ 216 \cdot 3 = 648 \][/tex]
Multiplying 216 by 3 does not provide the cube root. For Florence's answer to be correct, we would have:
[tex]\[ 648^3 = 216 \][/tex]
This statement is false, as [tex]\(648^3\)[/tex] is far greater than 216. Florence’s method and result of 648 are incorrect.
### Robi's Method
Robi claims the cube root of 216 is 6 because:
[tex]\[ 6^3 = 6 \cdot 6 \cdot 6 = 216 \][/tex]
To verify Robi’s answer, we calculate:
[tex]\[ 6^3 \][/tex]
[tex]\[ 6 \cdot 6 = 36 \][/tex]
[tex]\[ 36 \cdot 6 = 216 \][/tex]
Robi correctly identified that [tex]\(6^3 = 216\)[/tex], so his approach and result are correct.
### Conclusion
Among the three students, Robi found the correct cube root of 216, which is 6. The numerical evaluation confirms that:
[tex]\[ \sqrt[3]{216} = 5.999999999999999 \approx 6 \][/tex]
Therefore, Robi's cube root of 6 is correct, and he is the student who accurately found the cube root of 216.
