Using prime factorization to solve it, but am still stuck?
回答 (3)
2020-08-09 11:06 pm
✔ 最佳答案
1500k = 2² × 3 × 5³ × kIf 1500k is both a perfect square and a perfect cube,
the smallest value of 1500k = 2⁶ × 3⁶ × 5⁶
Hence, 2² × 3 × 5³ × (Smallest k) = 2⁶ × 3⁶ × 5⁶
Smallest k = 2⁴ × 3⁵ × 5³ = 486000
2020-08-09 10:54 pm
For a prime number to have a perfect square and perfect cube
the perfect number must be n⁶
n⁶ = (n²)³
n⁶ = (n³)²
-----------------------
Prime factors of 1500
5³ * 2² * 3
-----------------------
5⁶ = 5³ * 5³
2⁶ = 2² * 2⁴
3⁶ = 3 * 3⁵
Therefor
k = 5³ * 2⁴ * 3⁵
k = 486,000 <–––––––
the perfect number must be n⁶
n⁶ = (n²)³
n⁶ = (n³)²
-----------------------
Prime factors of 1500
5³ * 2² * 3
-----------------------
5⁶ = 5³ * 5³
2⁶ = 2² * 2⁴
3⁶ = 3 * 3⁵
Therefor
k = 5³ * 2⁴ * 3⁵
k = 486,000 <–––––––
2020-08-09 10:49 pm
Given that 1500k is both a perfect square and a perfect cube,
write down the smallest possible value of k.
write down the smallest possible value of k.
收錄日期: 2021-04-18 18:36:12
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https://hk.answers.yahoo.com/question/index?qid=20200809142128AA4QRfT