For square roots, if you think in terms of area, taking the square root of any area will give you the side length of a square with the same area.
For cube roots, instead of area, think in terms of volume. Taking the cube root of any volume will give you the side length of a cube with the same volume.
The relationship between scale factor and area is:
new area = old area x (scale factor)^2
Thus, to double the area of a shape, use a scale factor of square root of 2.
To triple the area of a shape, use a scale factor of square root of 3.
The relationship between scale factor and volume is:
new volume = old volume x (scale factor)^3
Thus, to double the volume of an object, use a scale factor of cube root of 2.
To triple the volume of an object, use a scale factor of cube root of 3.
If you need to know the square root of a number...the square root calculator is here to help you.