Question

What could be the possible one’s digit of the square root of the number \[5476\]?
A. 1 or 9
B. 2 or 8
C. 4 or 6
D. 3 or 7

Answer 1

Hint:
We shall begin by checking the value of the one’s digit of the given number. Then, we shall check the one’s digit in the square of the numbers in each of the options given in the question and compare.

Complete step by step solution:
\[\begin{array}{*{20}{l}}{{\rm{Th}}}&{\rm{H}}&{\rm{T}}&{\rm{O}}\\5&4&7&6\end{array}\]
In the number 5476, the value of one’s digit is 6. So, we have to check which number’s square has the same value as one’s digit in each of the options given.
A. We know that \[{1^2} = 1\] and \[{{\rm{9}}^2} = 81\].
Here, the value of the one’s digit is 1 and so this option is incorrect.
B. \[{2^2} = 4\] and \[{{\rm{8}}^2} = 64\]. Here, the value of one’s digit is 4 which is not the same as 6. So, we disregard this option.
C. Now we know that \[{4^2} = 16\] and \[{{\rm{6}}^2} = 36\]. The value of one’s digit is both 16 and 36 is 6, which is what we require. Hence, this is the correct option.
D. \[{3^2} = 9\] and \[{{\rm{7}}^2} = 49\]. The value of one’s digit, in this case, is 9 and this is not the value we require. We disregard this option as well.
$\therefore $ From the discussion above, we observe that either 4 or 6 have one’s digit as 6 in their squares. Hence, the square root of \[5476\] has either 4 or 6 in one’s place.

Therefore, the correct option is C.

Note:
We can verify the above discussion by finding the square root of \[5476\]. We observe that \[\sqrt {5476} = 74.\] Here, the square root has 4 in the one’s place. Thus, our finding is correct. A square root is a factor.