Question
Which number is a perfect cube?
Responses
A 360360
B 472472
C 512512
D 588
Responses
A 360360
B 472472
C 512512
D 588
Answers
GPT-4o mini
To determine which of the given numbers is a perfect cube, we can calculate the cube root of each number and see if it results in an integer.
1. **A: 360360**
- \( \sqrt[3]{360360} \approx 71.5 \) (not an integer)
2. **B: 472472**
- \( \sqrt[3]{472472} \approx 77.7 \) (not an integer)
3. **C: 512512**
- \( \sqrt[3]{512512} = 8 \times 16 \) = \( 8^3 = 512 \) (since \( 512128 = 8^3 \times 2^3 \))
4. **D: 588**
- \( \sqrt[3]{588} \approx 8.2 \) (not an integer)
After checking, the only perfect cube among the options is:
**C: 512512**
(Note: Upon calculation, the answer for the original number was an estimation here; to verify correctly would necessitate checking divisibility or systematic factorization.)
1. **A: 360360**
- \( \sqrt[3]{360360} \approx 71.5 \) (not an integer)
2. **B: 472472**
- \( \sqrt[3]{472472} \approx 77.7 \) (not an integer)
3. **C: 512512**
- \( \sqrt[3]{512512} = 8 \times 16 \) = \( 8^3 = 512 \) (since \( 512128 = 8^3 \times 2^3 \))
4. **D: 588**
- \( \sqrt[3]{588} \approx 8.2 \) (not an integer)
After checking, the only perfect cube among the options is:
**C: 512512**
(Note: Upon calculation, the answer for the original number was an estimation here; to verify correctly would necessitate checking divisibility or systematic factorization.)