$\text{a)}$

$\sqrt{125}-\sqrt{500}=\sqrt{25\cdot 5}-\sqrt{100\cdot 5}=$

$=\sqrt{25}\cdot \sqrt{5}-\sqrt{100}\cdot \sqrt{5}=5\sqrt{5}-10\sqrt{5}=-5\sqrt{5}$  

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$\text{b)}$

$\sqrt[3]{500}-\sqrt[3]{256}=\sqrt[3]{125\cdot 4}-\sqrt[3]{64\cdot 4}=$

$=\sqrt[3]{125}\cdot \sqrt[3]{4}-\sqrt[3]{64}\cdot \sqrt[3]{4}=5\sqrt[3]{4}-4\sqrt[3]{4}=\sqrt[3]{4}$