Question

Find the units digit of the cube root of the following number: 571787
(a). 5
(b). 4
(c). 3
(d). 7

Answer 1

Hint: In this question, we are asked to find the units place of the cube root of a given number. We should note that as in a multiplication, the units place of the product is given by the unit digit of the product of the units digits of the two numbers, therefore, the unit digit of the cube root of 571787 should be such that the cube of its units digit should yield a number with 7 in the units place. Thus, checking for all the digit’s cubes and using the above argument, we can obtain the required answer.

Complete step-by-step answer:

We know that when two numbers are multiplied, the units place in the product gets contribution only from the product of the units digits of the two numbers, therefore, the unit’s place of the product should be equal to of the product of the unit’s digits of the two numbers. Now, if the units digit of the cube root of 571787 is x, then from the above analogy,
Units place of ${{x}^{3}}$= Units place of 571787=7……………………..(1.1)
Now, as x is also a digit, it can only take values from 0 to 9. Therefore, we can individually check the cubes of the possible digits as follows
$\begin{align}
  & {{1}^{3}}=1 \\
 & {{2}^{3}}=8 \\
 & {{3}^{3}}=27 \\
 & {{4}^{3}}=64 \\
 & {{5}^{3}}=125 \\
 & {{6}^{3}}=216 \\
 & {{7}^{3}}=343 \\
 & {{8}^{3}}=512 \\
 & {{9}^{3}}=729 \\
\end{align}$
We find that the units digit of only ${{3}^{3}}$ is equal to 7……………..(1.2)
Therefore, from equations (1.1) and (1.2), we obtain the answer as 3 which matches option (c) of the question. Hence, (c) is the correct answer.

Note: We could also have calculated the answer by explicitly calculating the cube root which would have 83 and thus 3 in the units place. However, the trick used in the question gave us the same answer in a much easier and faster way.