The square root of 4,356 is an integer. without a calculator , determine what the integer is by eliminating possibilities.

It's more than 3600, so its greater than 60.
it's less than 4900, so its less than 70.
a no.'s root can end with six if the no. ends with 4 or 6.
so the no is either 64 or 66.
Now if it's 66, the square must be greater than sq of 65.
65 sq= 4225
the given no. is greater than sq of 65.
Therefore the number is 66.