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what is the sum of all whole numbers between 0 and 1000 that are both perfect squares and perfect cubes?

Sagot :

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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