Find the cube root of 17576 through elimination.

Hint:
Here, we will make groups of three digits starting from the rightmost digit of the given number. First group gives the one’s digit of the required cube root. Second group gives the ten’s digit of the required cube root. So, by applying this technique we will be able to get the cube root of the given number through estimation.

Complete step by step solution:
We have to make groups of three digits starting from the rightmost digit of 17576.
\[\underline {17} \] \[\underline {576} \]
So, one group has three digits i.e. 576 and the second group has two digits i.e. 17
The first group i.e. 576 will give us the one’ digit of the required cube root.
Since 576 ends with 6, so its cube root will also end with 6. As 6 comes in the unit’s place of a number only when its cube ends with 6. So the unit digit of the cube root is 6.
Now we will take the second group i.e. 17
As we all know that cube of \[{2^3} = 8\]and \[{3^3} = 27\] and we can clearly see that 17 lies between 8 and 27, i.e. \[{2^3} < 17 < {3^3}\]. We have to take the smaller number for ten’s place. So, we have to put 2 in the ten’s place.

Thus, the cube root of 17576 is 26.

Note:
The cube root of a number is the factor that we multiply by itself three times to get that number. We might get confused between the cube root and the square root. Square root of a number is the factor that we multiply by itself two times to get that number.
Square root is expressed as \[\sqrt[2]{{{\rm{number}}}}\].
Cube root is expressed as \[\sqrt[3]{{{\rm{number}}}}\].