### Theory:

You can use the following procedure if you know that the given number is a cube number.
Step 1: Choose any cube number.

Step 2: Start by forming groups of three digits from the number's rightmost digit. We get more than one group.

 $\begin{array}{l}\underset{¯}{\phantom{\rule{0.147em}{0ex}}\mathit{abc}\phantom{\rule{0.147em}{0ex}}}\\ \phantom{\rule{0.147em}{0ex}}↓\end{array}$ $\begin{array}{l}\underset{¯}{\phantom{\rule{0.147em}{0ex}}\mathit{def}\phantom{\rule{0.147em}{0ex}}}\\ \phantom{\rule{0.147em}{0ex}}↓\end{array}$ Second group First group

Step 3: The first group will give you the ones (or unit) digit of the required cube root. You can calculate this using the ending digit of the first group.

Step 4: Now, take the second group and find which two cube numbers this group lies. Choose the smallest cube number and find the cube root of that number. This is the tens place of the required cube root.

Step 5: Join the numbers we get in the first group and second group. This is the required cube root of the given number.
Example:
Find the cube root of the cube number $$79507$$.

Solution:

Step 1: The number $$79507$$ is a cube number.

Step 2: Now, split this number into two groups.

 $\begin{array}{l}\underset{¯}{\phantom{\rule{0.147em}{0ex}}79\phantom{\rule{0.147em}{0ex}}}\\ \phantom{\rule{0.147em}{0ex}}↓\end{array}$ $\begin{array}{l}\underset{¯}{\phantom{\rule{0.147em}{0ex}}507\phantom{\rule{0.147em}{0ex}}}\\ \phantom{\rule{0.147em}{0ex}}↓\end{array}$ Second group First group

Step 3: Let us take the first group, $$507$$. We know that "if a cube ends at $$7$$, then its cube root ends at $$3$$".

So, the ones place of the required number is $$3$$.

Step 4: The second group is $$79$$.

$$64 < 79 < 125$$

$$4^3 < 79 < 5^3$$

Here, the smallest cube number is $$64$$, and the cube root of $$64$$ is $$4$$.

So, the tens place of the required cube root is $$4$$.

Step 5: The required cube root is $$43$$.

Therefore, $$\sqrt[3]{79507}$$ $$=$$ $$43$$.