Question

What can be the units place digit in the square roots of the following numbers:
1.9604
2.65536
3.998001
4.60481729

Answer 1

Hint: The required number(s) will be the number(s) whose square will have the same unit’s digit as the unit place of the given number in the question.
To find the unit’s place digit of the square root of the given number, we will find the squares of all elementary numbers which are from 1 to 9. After that we will list out all the numbers whose square’s unit’s digit is same as the unit’s digit in the question. We will be doing this because the square of the square root’s unit digit will always be equal to the unit’s digit of the full number’s square.

Complete step by step answer:
The square of each digit is given as
${1^2}\; = 1$
Unit place digit= 1
\[{2^2} = 4\]
Unit place digit=4
\[{3^2} = 9\]
Unit place digit=9
\[{4^2} = 16\]
Unit place digit=6
\[{5^2} = 25\]
Unit place digit=5
\[{6^2} = 36\]
Unit place digit=6
\[{7^2} = 49\]
Unit place digit=9
\[{8^2} = 64\]
Unit place digit=4
\[{9^2} = 81\]
Unit place digit=1

1)9604
In the number we can see the unit digit is 4 and as we know the square root’s unit digit is always equal to the unit's digit of the full number’s square.
So the units place digit in the square root of \[9604\] is $2\,and\,8$
2) 65536
In the number we can see the unit digit is 6 and as we know the square root’s unit digit is always equal to the unit's digit of the original number’s square.
So the units place digit in the square root of \[65536\] is $4\,and\,6$
3) 998001
In the number we can see the unit digit is 1 and as we know the square root’s unit digit is always equal to the unit's digit of the original number’s square.
So the units place digit in the square root of \[998001\] is $1\,and\,9$
4)60481729
In the number we can see the unit digit is 9 and as we know the square root’s unit digit is always equal to the unit's digit of the original number’s square.
So the units place digit in the square root of \[60481729\] is $3\,and\,7$

Note: We can also solve this question by finding the exact square root of each number. After finding the square root of each number we will get the unit’s digit which will be the answer to your question. But this method will be much lengthy and can waste a lot of time as it would require factors.