Square Roots and Area


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.


Cube Roots and Volume


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.


Square Roots and Scale Factor


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.


Cube Roots and Scale Factor


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.



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