what is a cube root

Question

X^2 + (y - <cube root> X^2)^2 = 1

Answer 1

If z=∛x, then z is the cube root of x, and x=z³. z³ is another way of writing z×z×z, that is, z multiplied by itself three times.

Example: If x=64=4×4×4, then z=4, making 4 the cube root of 64.

The equation x²+(y-∛x²)²=1 can also be written x²+(y-x^⅔)²=1.

This can be expanded: x²+y²-2x^⅔y+x^4/3=1, but since there are two variables x and y and only one equation, this is a relationship and there are an infinite number of solutions (i.e., values of x and y) satisfying the relation. The equation can be used for drawing a graph. The graph is a cardioid (heart shape):

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