Question

What will be the unit digit of the squares of the following number?
(i) 81
(ii) 272
(iii) 799
(iv) 3853
(v) 1234
(vi) 26387
(vii) 52698
(viii) 99880
(ix) 12796
(x) 55555

Answer 1

Hint: Take the numbers one – by – one and multiply the unit digit with the same unit digit. Check the digit we are getting at the unit place of the number obtained by multiplication. This will be the unit digit of the square of the given number.

Complete step by step answer:
We have been provided with a certain number and we have to find the unit digit of the squares of given number. Well, these numbers are very large to find their squares so that will not be an appropriate method.
Actually, the unit digit can be obtained by multiplying the unit digit of a chosen number with the same unit digit. The unit digit of the number formed by this multiplication will be our answer. Let us find the answers for each of the following.
(i) 81
Here, the unit digit is 1. So, multiplying 1 with 1, we get 1. So, the unit digit of square of 81 will be 1.
(ii) 272
Here, the unit digit is 2. So, multiplying 2 with 2, we get 4. So, the unit digit of the square of 272 will be 4.
(iii) 799
Here, the unit digit is 9. So, multiplying 9 with 9, we get 81 whose unit digit is 1. So, the unit digit of the square of 799 will be 1.
(iv) 3853
Here, the unit digit is 3. So, multiplying 3 with 3, we get 9. So, the unit digit of the square of 3853 will be 9.
(v) 1234
Here, the unit digit is 4. So, multiplying 4 with 4, we get 16 whose unit digit is 6. So, the unit digit of the square of 1234 will be 6.
(vi) 26387
Here, the unit digit is 7. So, multiplying 7 with 7, we get 49 whose unit digit is 9. So, the unit digit of the square of 26387 will be 9.
(vii) 52698
Here, the unit digit is 8. So, multiplying 8 with 8, we get 64 whose unit digit is 4. So, the unit digit of the square of 52698 will be 4.
(viii) 99880
Here, the unit digit is 0. So, the unit digit of the square of 99880 will be 0.
(ix) 12796
Here, the unit digit is 6. So, multiplying 6 with 6, we get 36 whose unit digit is 6. So, the unit digit of the square of 12796 will be 6.
(x) 55555
Here, the unit digit is 5. So, multiplying 5 with 5, we get 25 whose unit digit is 5. So, the unit digit of the square of 55555 will be 5.

Note: One may note that these are very large numbers and finding the squares of these numbers will take a long time. So, never try to square the numbers because it is not necessary for finding the unit digit. If they would have asked to find $$3^{rd}$$ or $$4^{th}$$ digit then we would have left with no other options but to square.