1728 = 2 x 864 = 2x2 x 432 = 2x2x2 x 216 = 2x2x2 x 2 x 108 = 2x2x2 x 2x2 x 54 = 2x2x2 x 2x2x2 x 27 = 2x2x2 x 2x2x2 x 3 x 9 = 2x2x2 x 2x2x2 x 3x3x3 = 2x2x3 x 2x2x3 x 2x2x3 = 12 x 12 x 12
cube root = 12
To find the smallest value of k when 882k is a cube, we need to factor out the cube from 882k. The prime factorization of 882 is 2 x 3^2 x 7^2. For 882k to be a cube, we need to find the smallest value of k such that the exponent of each prime factor in the prime factorization of 882k is a multiple of 3. Therefore, the smallest value of k would be 2^2 x 3 x 7 = 84.
33 = 81 63 = 216 93 = 729 and 123 = 1728
The cube root of this number is one more than the smallest prime
k = 98. In the prime factorization (in power format) of a perfect cube, every prime must be to the power of a multiple of 3. 756 = 2^2 x 3^3 x 7 Thus the smallest perfect cube that is a multiple of 756 is 2^3 × 3^3 × 7^3; to obtain this need to multiply 756 by 2^1 × 3^0 × 7^2 = 98 Thus the smallest k to make 756k a perfect prime is k = 98.
6
2^6 = 64 The cube root is 2^2, or 4
The prime factorization for 125 is:5 X 5 x 5125 is the cube of 55x5x5
25
The cube root of 1728 is: 121728 cubed is: 5,159,780,352
1728 is even so it cannot have an odd cube root.
the cube root of 1728 is 12
Because 123 = 1728
If a factor appears 3 times, you get this factor (only once) times the cube root of a smaller number (the original number divided by the factor cubed).
12
To find the number that, when multiplied by itself three times, equals 1728, you need to calculate the cube root of 1728. The cube root of 1728 is 12, since 12 × 12 × 12 = 1728. Therefore, the number is 12.
Volume of cube: 12*12*12 = 1728 cubic inches
1728 cubic inches