Question

Let m be the side length of the fourth smallest possible square with integer value of its area, and let n be the sum of all prime numbers less than 10. Find MN(N-M).

Answer 1

Answer:

510

Step-by-step explanation:

It's assumed 0 is not an integer.

M is obviously 2. The area of a square is the square of its side length. If this area must be an integer, then it must be the fourth integer, which is 4. The side length, $M=\sqrt{4} = 2$

A prime number is a positive integer which can be divided exactly by only itself and 1. In fact, it has only those two factors. The last statement excludes 1 as a prime number. Hence, the prime numbers less than 10 are 2, 3, 5 and 7. Their sum is $N=2+3+5+7=17$.

To evaluate $MN(N-M)$,

$2\times17(17-2)=34\times15=510$