The number 1 is a perfect square (1X1=1) and a perfect cube (1X1X1=1). What is the next smallest whole number which is both a perfect square and a perfect cube?
64 = 8^2 = 4^3
2^6 = (2^3)^2 = (2^2)^3
man what
To find the next smallest whole number that is both a perfect square and a perfect cube, we can start by finding the smallest perfect square greater than 1. Since the square of 2 is 4, and 2 is the smallest whole number greater than 1, the smallest perfect square greater than 1 is 4.
Next, we need to find the smallest perfect cube greater than 1. Again, starting with 2, the cube of 2 is 8, so 2 is the smallest whole number greater than 1 that is a perfect cube.
Now we can check if any of the numbers between 2 and 8 are both perfect squares and perfect cubes. Checking each number, we find that neither 3 nor 5 are perfect squares or perfect cubes. However, 6 is both a perfect square (2 x 2 = 4) and a perfect cube (2 x 2 x 2 = 8).
Therefore, the next smallest whole number that is both a perfect square and a perfect cube is 6.