Question

how many perfect cube and perfect square between 2000 and 7000

Answer 1

16=116=1

26=6426=64

36=72936=729

46=409646=4096

Welp, there you go. The answer is 4096.

4096=(42)3=163=(43)2=6424096=(42)3=163=(43)2=642

If you wanna know the more mathematical way of doing this sort of thing, you can find the highest number that, when raised to the sixth, is less than 7000 by taking the sixth root of 7000 and truncating the decimal. You can also find the smallest number that, when raised to the sixth, is greater than 2000 by taking the sixth root of 2000 and rounding up.

7000−−−−√6≈4.37470006≈4.374

2000−−−−√6≈3.55020006≈3.550

And for anyone wondering where I got 6 from, it’s the least common multiple of 2 and 3.

Answer 2

Hi User! here is your answer...

Answer:

1 number=4069

Step-by-step explanation:

(3^2)^3=729            729<2000

(4^2)^3=4069             2000<4069>7000

(5^2)^3=15625             7000<15625

Hence, the only number which is a perfect cube & square, and is between 200 and 7000 is 4069

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