A Square and A CubeClass 8 Mathematics Assertion & Reason Questions

Assertion (A): Locker #81 will remain open at the end of the process described in the puzzle.

Reason (R): A locker remains open if it is toggled an odd number of times, which occurs only for locker numbers that are perfect squares as they have an odd number of factors.

Assertion (A): The number 45678 is a perfect square.

Reason (R): A number ending in 2, 3, 7, or 8 is never a perfect square.

Assertion (A): The sum of the first 6 odd natural numbers, $1+3+5+7+9+11$, is 36.

Reason (R): The sum of the first $n$ odd natural numbers is given by the formula $n^2$.