Cube root

Newton's method for cube roots is based on the fact that if y is an approximation to the cube root of x, then a better approximation is given by the value

x/(y * y) + 2y

Use this formula to implement a cube-root procedure analogous to the square-root procedure. In section 1.3.4 we will see how to implement Newton's method in general as an abstraction of these square-root and cube-root procedures.)

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(check-equal? (round (* 1000 (cube-root 8.0))) 2000.0)
(check-equal? (round (* 1000 (cube-root 1000.0))) 10000.0)
(check-equal? (round (* 1000 (cube-root 1000000000.0))) 1000000.0)
(check-equal? (round (* 1000 (cube-root 0.008))) 200.0)