A Ridiculously Small Difference

Let $[\cdot]$ represents the symbol in this equation. We can wrote $\sqrt[10]10\:[\cdot]\:\sqrt[3]2$ , then, we just exponent by 30. We will get $(\sqrt[10]10)^{30}\:[\cdot]\:(\sqrt[3]2)^{30}\Rightarrow 1000 < 1024$ Hence $\sqrt[10]10 < \sqrt[3]2$