Roots Rules

<a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-roots-rules">Roots Rules Exercise</a>There are several Roots Rules that we have to remember. <ul> <li>First rule: an exponent can "cancel" a root out.</li> </ul> $$(\sqrt{a})^2 = a$$ $$(\sqrt[5]{7})^5 = 7$$ <ul> <li>Second rule: alternatively, a root can "cancel" an exponent out.</li> </ul> $$\sqrt{6^2} = 6$$ $$\sqrt[3]{x^3} = x$$ $$\sqrt{x^2} = |x|$$ <ul> <li>Third rule: if you multiply two roots together (of the same order root), you can combine what's under the radicals together:</li> </ul> $$\sqrt{a}\sqrt{b} = \sqrt{ab}$$ $$\sqrt{5}\sqrt{7} = \sqrt{5 \times 7}= \sqrt{35}$$ <ul> <li>Fourth rule: if you divide one root by another (of the same order root), you can combine what's under the radicals:</li> </ul> $$\frac{\sqrt{12}}{\sqrt{3}} = \sqrt{\frac{12}{3}}=\sqrt{4} = 2$$