The inverse of cubing a number is applying cubic root
[tex]a^3\leftrightarrow\sqrt[3]{a}[/tex]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,
[tex]\sqrt[]{225}=15[/tex]Because
[tex]\begin{gathered} 15\times15=225 \\ 15^2=225 \end{gathered}[/tex]This way,
[tex]\begin{gathered} \sqrt[]{49}=7\Leftrightarrow7^2=49 \\ \sqrt[]{121}=11\Leftrightarrow11^2=121 \\ \sqrt[]{1600}=40\Leftrightarrow40^2=1600 \end{gathered}[/tex]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,
[tex]\sqrt[3]{64}=8[/tex]Because
[tex]\begin{gathered} 8\times8\times8=64 \\ 8^3=64 \end{gathered}[/tex]Therefore,
[tex]\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}[/tex]