The inverse of cubing a number is applying cubic root
![a^3\leftrightarrow\sqrt[3]{a}](https://img.qammunity.org/2023/formulas/mathematics/college/z7yic4azttyqx6u23hyhy3btu85hacnezr.png)
Now, let's go through the examples:
When you want to find the square root of a number x you have to ask yourself:
Which number, when multiplied by itself, will give me x ?
For example,
![\sqrt[]{225}=15](https://img.qammunity.org/2023/formulas/mathematics/college/gk0h7ppj12gid8u9h1o2cl9v7vf1bghldx.png)
Because

This way,
![\begin{gathered} \sqrt[]{49}=7\Leftrightarrow7^2=49 \\ \sqrt[]{121}=11\Leftrightarrow11^2=121 \\ \sqrt[]{1600}=40\Leftrightarrow40^2=1600 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/ips7zv4fafagnjejx3uay6f1y49az9jejk.png)
Now for the cubic root:
When you want to find the cubic root of a number y you have to ask yourself:
Which number, when multiplied by itself two times, will give me y ?
For instance,
![\sqrt[3]{64}=8](https://img.qammunity.org/2023/formulas/mathematics/college/dy8er5e0p9ryk0mr0tch36zs6bhbn88kh8.png)
Because

Therefore,
![\begin{gathered} \sqrt[3]{8}=2\Leftrightarrow2^3=8 \\ \sqrt[3]{1}=1\Leftrightarrow1^3=1 \\ \sqrt[3]{2744}=14\Leftrightarrow14^3=2744 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/j5wynj42agg0wtan4suiuc7oi6hfe8xv4u.png)