Question

Find the cube root of the number 91125 by looking at the last digit and using estimation?

Answer 1

Hint: Divide the number into two groups, the last three digits in one group and the first two digits in the other group then pick the group which has the last three digits (here 125) and then select a number from 1 to 9 so that its unit digit of the cube will be 5 then taking the other group which has first two digits, now cubing the numbers from 2 and then see which cube of the number is less than or equal to 91.

Complete step-by-step solution:
First of all, divide the given number 91125 into two groups.
91125
The bold part of the above number i.e. 125 is in group 1 and the underlined part of the number i.e. 91 is in group 2.
We have asked to find the cube root of 91125 so first, we are going to find the unit place of the cube root of 91125 as follows:
Take the number 125. Now take the cube of the number from 2 to 9 and see which number on cubing will give 5 as a unit digit.
Cubing of 5 is $5\times 5\times 5=125$.
As you can see the unit digit of the cube of 5 is 5 so the unit digit of the cube root of 91125 is 5.
Now, we are going to find the tens place value of the cube root of 91125.
Take the other group of the number 91125 which is 91. Now, take the cube from number 2 onwards and then see cubing of which number gives 91 or less than 91.
${{2}^{3}}=8,{{3}^{3}}=27,{{4}^{3}}=64,{{5}^{3}}=125$
91 lies between ${{4}^{3}}$ and ${{5}^{3}}$ so ${{4}^{3}}$ is a number which is less than 91 so the tens place value of cube root of 91125 is 4.
Hence, the cube root of 91125 is 45.

Note: You can check whether the cube root which we have found above is correct by multiplying the cube root of 91125 three times by itself and see if we are getting the value of the cube as 91125 or not.
Multiplying 45 three times we get,
$\begin{align}
  & \Rightarrow 45\times 45\times 45 \\
 & =2025\times 45 \\
 & =91125 \\
\end{align}$
As you can see we are getting the same result of the cube of 45 as given in the above problem so the cube root which we have found for 91125 is correct.