Question

Which among ${43}^2,{67}^2,{52}^2,{59}^2$ would end with digit $1$?
[2 marks]
[Properties of Square Numbers]

Answer 1

Solution:
We know that, the unit digit of the square of a natural number is the unit digit of the square of the digit at unit place of the given natural number.
[0.5 mark]

Now, we can find the unit digit of squares of the given numbers.
Unit digit of ${43}^2=9$, because unit digit of $3^2$ is $9$.
Unit digit of ${67}^2=9$, because unit digit of $7^2$ is $9$.
Unit digit of ${52}^2=4$, because unit digit of $2^2$ is $4$.
Unit digit of ${59}^2=1$, because unit digit of $9^2$ is $1$.
[1 mark]

Clearly the square of 59${}^2$ ends with unit digit $1$.
[0.5 mark]