Find the order

Learning Objectives Define the 'order' (or index) of a radical expression. Identify the order and radicand for any given radical. Convert radicals to equivalent forms with a common order using the least common multiple (LCM). Compare the magnitude of two or more radical expressions with different orders. Arrange a set of radical expressions in ascending or descending order. Apply the concept of order to solve problems involving inequalities with radicals. Which is larger, $\sqrt{7}$ or $\sqrt[3]{30}$? 🤔 It's not obvious just by looking! This lesson gives you the tools to find out for sure. In this tutorial, you'll learn that the 'order' of a radical is its root number (like square root or cube root). We will master a method to find a 'com...

TermDefinitionExample Radical ExpressionAn expression that contains a root symbol ($\sqrt{\phantom{x}}$). The entire expression is called a radical.$\sqrt{25}$ and $\sqrt[3]{x-4}$ are both radical expressions. Order (or Index)The small number written in the 'v' of the radical symbol. It tells you which root to take. If no number is written, it is an implied order of 2 (a square root).In $\sqrt[5]{32}$, the order is 5. In $\sqrt{9}$, the order is 2. RadicandThe number, variable, or expression written inside the radical symbol.In $\sqrt[3]{64}$, the radicand is 64. Rational ExponentAn alternative way to write a radical expression using a fractional exponent.$\sqrt[n]{a}$ is the same as $a^{1/n}$. So, $\sqrt[3]{8}$ is equivalent to $8^{1/3}$. Common OrderA shared order that two or...

The Comparison Rule If $a > b > 0$, then $\sqrt[n]{a} > \sqrt[n]{b}$. Use this rule after you have converted radicals to a common order. It states that for two radicals with the same order, the one with the larger radicand is the larger number. The Order Conversion Formula $\sqrt[n]{a^m} = \sqrt[n \cdot p]{a^{m \cdot p}}$ This is the key formula for changing the order of a radical. To get a new order, you multiply the original order (n) by a number (p). To keep the expression equivalent, you must also multiply the exponent of the radicand (m) by that same number (p).