# Rational Approximation of numbers

$$S = \sqrt [ 3 ]{ 10 }$$

Define $$P = \dfrac{a}{b}$$, where $$a,b$$ are natural numbers less than $$1000$$

Find $$a+b$$ such that $$P$$ has a value closest to $$S$$, or mathematically $$|P-S|$$ is minimised

$$a,b$$ are co-prime natural numbers.

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