Answer:
The least number that should be subtracted from 1456 to make a perfect square with formula is 9^2, which is equal to 81.
Explanation:
To find the least number that should be subtracted from 1456 to make a perfect square with formula, we need to use the formula for the square of a number.
(n + a)squared = nsquared + 2nas + asquared
In our case, since we want to find the least number to be subtracted, we need to make the result of the formula 2nas + asquared negative (so the difference is a perfect square)
2nas + asquared < 0
Let's try for some values of n:
1456 - n = aperfect square
1456 - 5^2 = (1456 - 25)^2 = 1431^2
1456 - 7^2 = (1456 - 49)^2 = 1407^2
1456 - 9^2 = (1456 - 81)^2 = 1375^2
Since 1375^2 is the smallest of the squares calculated so far, we can conclude that the smallest number that should be subtracted from 1456 to make a perfect square formula with a perfect square result is 1456 - 9^2 == 1456 - 81 == 9^2 == 81
So in this case, the least number that should be subtracted from 1456 to make a perfect square with formula is 9^2, which is equal to 81.