The number 1 is a perfect square and a perfict cube. What is the next smallest whole number which is a perfect square and a perfect cube?
To find the next smallest whole number that is both a perfect square and a perfect cube, we can start by understanding what it means for a number to be a perfect square and a perfect cube.
A perfect square is a number that can be obtained by multiplying an integer by itself. For example, 4 is a perfect square because it can be obtained by multiplying 2 by 2 (2 * 2 = 4). Similarly, 9 is a perfect square because it can be obtained by multiplying 3 by 3 (3 * 3 = 9).
A perfect cube is a number that can be obtained by multiplying an integer by itself twice. For example, 8 is a perfect cube because it can be obtained by multiplying 2 by 2 by 2 (2 * 2 * 2 = 8). Similarly, 27 is a perfect cube because it can be obtained by multiplying 3 by 3 by 3 (3 * 3 * 3 = 27).
Now let's find the next smallest whole number that is both a perfect square and a perfect cube:
Starting from number 2, we need to check if it satisfies both conditions. We can calculate its square and cube values:
For number 2:
Square: 2 * 2 = 4
Cube: 2 * 2 * 2 = 8
Since 2 is not a perfect square, we move on to the next number.
For number 3:
Square: 3 * 3 = 9
Cube: 3 * 3 * 3 = 27
Number 3 satisfies both conditions and is the next smallest whole number that is both a perfect square and a perfect cube.
Therefore, the answer is 3.