Question

The remainder of any perfect aqure
divided by 3 is​

Answer 1

Answer:

The remainder of any perfect square divided by 3 is 1 if not divisible by 3

Step-by-step explanation:

Let Divide the number in three categories

(3n)² , (3n+1)² , (3n+2)²

(3n)² = 9n² = 3 * 3n²  

Hence divisible by 3

Remainder = 0

(3n + 1)² = 9n² + 6n + 1

= 3 * n(3n + 2) + 1

Remainder = 1

(3n + 2)² = 9n² + 12n  + 4

= 9n² + 12n + 3 + 1

= 3(3n² + 4n + 1) + 1

Remainder = 1

The remainder of any perfect square divided by 3 is 1 if not divisible by 3