the sum of the numbers are 794.
The numbers are 1, 64 and 729.
Let the required number be N.
Let N be a perfect square of A.
We have A^2=N. —(1)
Let N be a perfect cube of B.
We have B^3=N. —(2)
From (1) and (2) we get:
B=A^(2/3)
For B to e an integer, A must be the cube of some other integer (say C).
Therefore,
A=C^3
B=C^2
Now, starting with C = 1
A = 1
B = 1
N = 1
For C = 2
A = 8
B = 4
N = 64
For C = 3
A = 27
B = 9
N = 729.
therefore sum=794.
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