Simplifying Roots

<a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-simplifying-roots">Simplifying Roots Exercise</a>You can Simplify Roots, which is pretty cool. That means "pulling out" something from under the radical, and thereby making the number under the radical smaller. Here's how it works: <ul> <li>If you're taking the square root of a number, check if there are any perfect square factors in the number. If you're taking the cube root of a number, check if there are any perfect cube factors in the number. If you're taking the fourth root of a number, check if there are any perfect powers of $4$ in the number. You get the idea.</li> </ul> $$\sqrt{32}=\sqrt{16 \cdot 2}= \sqrt{4^2 \cdot 2 }$$ $$\sqrt[3]{56}=\sqrt[3]{8 \cdot 7}= \sqrt[3]{2^3 \cdot 7}$$ $$\sqrt[4]{405}=\sqrt[4]{81 \cdot 5}= \sqrt[4]{3^4 \cdot 5}$$ <ul> <li>Next, "pull" the perfect square or perfect cube (or whatever) out.</li> </ul> $$\sqrt{4^2 \cdot 2}=\sqrt{4^2}\sqrt{2}=4\sqrt{2}$$ $$\sqrt[3]{2^3 \cdot 7}=\sqrt[3]{2^3}\sqrt[3]{7}=2\sqrt[3]{7}$$ $$\sqrt[4]{3^4 \cdot 5}=\sqrt[4]{3^4}\sqrt[4]{5}=3\sqrt[4]{5}$$