Question

Find the cube root of the given number through estimation:
5832

Answer 1

Hint: In this question use the concept that since the last digit of 5832 is 2 thus we need to flip it with 8, and then we need to cut 3 numbers from right involving the last digit. Now we need to find the number whose cube is closest to the remaining digits. This number fits to the left most digit and the replacement of 2 with 8 fits to the right most digit.

Complete step-by-step solution -
The cube root of 5832 through estimation is given below.
First of all we need to remember all the cube roots of numbers from 1 to 10, another thing that we need to remember is if the last digit of the number whose cube is to find is 1, 4, 5, 6, 9 ,0 then let it be same and if it is 2, 8 ,3 and 7 then flip $2\leftrightarrow 8\text{ and 3}\leftrightarrow \text{7}$. Cut the last three numbers from the left of the number whose cube is to be found and then for the remaining numbers figure out the number whose cube is closest to that number.

So, the cube root of 5832 is
Last digit is 2 so we have to replace 2 with 8 thus now we have 8,
Thus the unit place of the cube root of 5832 is 8.
Now cut three digits from left of 5832 hence only 5 is left,
The closest cube root to 5 is of 1 see from the table.
Thus the tens place of cube root of 5832 is 1.
Hence the answer is 18.
$\Rightarrow \sqrt[3]{5832}=18$
So this is the required answer.

Note: There can be another method to find the cube root of any number as we know that cube root of any number p is, so do the prime factorization of this number p so as to make its factor satisfy the condition of $p^{{\displaystyle \frac{1}{3}}}$, the simplified form after power evaluation will be the answer.