We are given the following radical
![\sqrt[]{243}](https://img.qammunity.org/2023/formulas/mathematics/college/xbxsfjksv261k5r3ncu206kaqhk106cm85.png)
Let us reduce the above radical
We need to break the number 243 into a product of factors
Notice that 81 and 3 are the factors (83×3 = 243)
![\sqrt[]{243}=\sqrt[]{81}\cdot\sqrt[]{3}](https://img.qammunity.org/2023/formulas/mathematics/college/l10f2qxzzgr7lixz7om7gt5ujci1oadgn2.png)
Since 81 is a perfect square so the radical becomes
![\sqrt[]{243}=\sqrt[]{81}\cdot\sqrt[]{3}=9\cdot\sqrt[]{3}](https://img.qammunity.org/2023/formulas/mathematics/college/1ut8yof2vuth4p7vf1lky279rqel6zcrot.png)
Therefore, the simplified radical is
![undefined]()