# It was a Saturday!

Algebra Level 5

$21x^3+5y^2+2016z^2$

Given that $$x,y$$ and $$z$$ are positive real numbers satisfying $$xyz=\dfrac{5\sqrt{70}}{\sqrt[3]{3}}$$. It is known that the minimum value of the above expression is $$a\sqrt{b}$$, where $$a$$ and $$b$$ are positive integers with $$b$$ square-free. Find $$a+b$$.

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