What is the value of $\sqrt{1,\!000,\!000} - \sqrt[3]{1,\!000,\!000}$?
I notice that both expressions under the radicals are powers of 10, so I can use the properties of exponents and roots to simplify them. For the square root, I can rewrite $1,\!000,\!000$ as $10^6$, and then use the rule that $\sqrt{x^a} = x^{a/2}$ to get $\sqrt{1,\!000,\!000} = \sqrt{10^6} = 10^3 = 1,\!000$. For the cube root, I can do a similar thing and rewrite $1,\!000,\!000$ as $10^6$, and then use the rule that $\sqrt[3]{x^a} = x^{a/3}$ to get $\sqrt[3]{1,\!000,\!000} = \sqrt[3]{10^6} = 10^2 = 100$. Now I have $\sqrt{1,\!000,\!000} - \sqrt[3]{1,\!000,\!000} = 1,\!000 - 100 = 900$. 