2007-01-29 02:13:22 · 12 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
729
2007-01-29 02:20:34 · answer #1 · answered by fcas80 7 · 2⤊ 1⤋
a^2 = b^3 ==> a > b and a and b > 0
100 <= a^2 <= 999
sqrt(100) <= a <= sqrt(999)
10 <= a <= 31.606961258...
a must be a perfect cube between 10 and 31
==> 27
100 <= b^3 <= 999
cbrt(100) <= b <= cbrt(999)
4.641588... <= b <= 9.996665554937...
b must be a perfect square between 4.6 and 9.9
==> 9
a^2 = b^3
==> 27^2 = 9^3
==> 729 = 729 the only 3 digit number both a perfect square and a perfect cube
If you want all perfect squares which are perfect cubes. (x^2)^3 = (x^3)^2
x^6 = x^6
plug in 1 ==> (1^2)^3 = (1^3)^2
1^3 = 1^2
1 = 1
2 ==> (2^2)^3 = (2^3)^2
4^3 = 8^2
64 = 64
4 ==> (4^2)^3 = (4^3)^2
16^3 = 64^2
4096 = 4096
2007-01-29 04:30:58 · answer #2 · answered by bjs820 2 · 1⤊ 0⤋
Square Perfect
2016-10-07 02:12:08 · answer #3 · answered by ? 4 · 0⤊ 0⤋
If a number is a square and a cube it is a 6th power.
The only 3 digit 6th power is 3^6 = 729
2007-01-29 05:25:37 · answer #4 · answered by steiner1745 7 · 1⤊ 0⤋
You simply square a cubed number or cube a squared number. In this case, 729 sounds good. It is 27^2 or 9^3.
2007-01-29 02:19:03 · answer #5 · answered by Harappy 1 · 2⤊ 1⤋
100 is a perfect square 10^2=100
100 is a perfect cube 10^3=100
2007-01-29 03:23:01 · answer #6 · answered by Dave aka Spider Monkey 7 · 0⤊ 2⤋
729=9^3=27^2
2007-01-29 02:19:39 · answer #7 · answered by bruinfan 7 · 2⤊ 1⤋
5 digit extensive style ought to be divisible by skill of two and by skill of three. utilising those 2 numbers you need to make your techniques up the right powers. 0.5 the 5 digit extensive style is a suitable cube. so the skill of two ought to be a different of three plus one (cube and then 0.5 of the extensive style). Numbers that greater healthful are 4, 7, 10. the skill of three ought to be a different of three. 3, 6, or 9. Now, a third of the 5 digit extensive style is a suitable sq.. So, the skill of three ought to be a different of two plus one million (sq. then one third of the extensive style). Numbers that greater healthful are 3, 5, 7, 9. the skill of two ought to be a different of two. Numbers that greater healthful are 2, 4, 6, 8, 10. you need to now see that shall we've 2^4 or 2^10 and the two 3^3 or 3^9. So, attempting 2^4*3^3 and we get 432, no longer great sufficient. 2^4*3^9 provides us 314928, that's basically too enormous. 2^10*3^3 provides us 27648, that's a 6 digit extensive style. So, 27,648 is your answer.
2016-11-28 02:46:40 · answer #8 · answered by bernabeu 4 · 0⤊ 0⤋
729...27^2 = 9^3 = 729
2007-01-29 02:24:54 · answer #9 · answered by In-Sync 3 · 1⤊ 1⤋
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2016-08-20 06:24:22 · answer #10 · answered by Anonymous · 0⤊ 0⤋