On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of this number is divided by 5?

Question: On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of this number is divided by 5?

Solution:
Let,
The number be x
And on dividing x by 5, we get p as quotient and 3 as remainder
∴ x = 5p + 3
or, x² = (5p + 3)²
= 25p² + 30p + 9
= 25p² + 30p + 5 + 4
= 5(5p² + 6p + 1) + 4
∴ On dividing the square of this number by 5, we get the remainder as 4.