Let the larger number = xThen the square of the smaller number = 8 times the larger number = 8xand the square of the larger numbe r = xAccording to the question,x - 8x = 180=> x - 8x - 180 = 0=> x - 18x + 10x - 180 = 0=> x(x - 18) + 10(x - 18) = 0=> (x - 18) (x + 10) = 0=> x - 18 = 0 or x + 10 = 0=> x = 18 or x = -10Thus, the larger number = 18 or -10Then, the square of the smaller number = 8(18) or 8(-10)= 144 or -80The square of a number can't be negative, so, the square of smaller number = 144Hence, the smaller number = sqrt(144) = 12The numbers are 12 and 18

Let the larger number = xThen the square of the smaller number = 8 times the larger number = 8xand the square of the larger numbe r = xAccording to the question,x - 8x = 180=> x - 8x - 180 = 0=> x - 18x + 10x - 180 = 0=> x(x - 18) + 10(x - 18) = 0=> (x - 18) (x + 10) = 0=> x - 18 = 0 or x + 10 = 0=> x = 18 or x = -10Thus, the larger number = 18 or -10Then, the square of the smaller number = 8(18) or 8(-10)= 144 or -80The square of a number can't be negative, so, the square of smaller number = 144Hence, the smaller number = sqrt(144) = 12The numbers are 12 and 18 .

12 and 18 is the right answer