Question

What will be the unit digit of the square of 799?
a) 1
b) 8
c) 0
d) 6

Answer 1

Hint:- We can find out the unit’s digit of the square of any number just by looking at the unit’s digit of the number whose square is to be calculated. Use the fact that the square of any number ends in the same digit as the square of the number at the unit's place ends.

Complete step-by-step answer:

The unit’s digit of the square of the number 799 can be identified as follows:-

The unit digit of a perfect square can be only 0, 1, 4, 5, 6 or 9. Which means that 2, 3, 7, 8 can never be the unit digit of any perfect square.

Now, let us find the unit digit of the square of the number 799.

So, here is a fact that the unit digit of the square of any number ending with a 1 or a 9 will always be 1. This can be explained as follows:-

We know that \[1\times 1\] is always 1 and \[9\times 9\] is always 81. Here, we can also observe that the unit’s digit of the squares of 1 and 9 is also 1.

Note:- The square of a number having:

1 or 9 at the units place ends in 1.
2 or 8 at the unit's place ends in 4.
3 or 7 at the unit's place ends in 9.
4 or 6 at the unit's place ends in 6.
5 at the unit's place ends in 5.

One must remember these facts.

We know that \[1\times 1\] is always 1 and \[9\times 9\] is always 81. The unit’s digit of the squares of 1 and 9 is also 1. Therefore, the unit’s digit of the square of the numbers having 1 and 9 as their unit’s digit is always 1.

We know that \[1\times 1\] is always 4 and \[8\times 8\] is always 64. The unit’s digit of the squares of 2 and 8 is also 4. Therefore, the unit’s digit of the square of the numbers having 2 and 8 as their unit’s digit is always 4.

We know that \[3\times 3\] is always 9 and \[7\times 7\] is always 49. The unit’s digit of the squares of 3 and 7 is also 9. Therefore, the unit’s digit of the square of the numbers having 3 and 7 as their unit’s digit is always 9.

Etc.