A number is greater than the square of 44 but smaller than the square of 45. If one part of the number is the square of 6 and the number is a multiple of 5, then find the number.?

Let the number be x.
44² < x < 45²
⇒ 1936 < x < 2025 ...(i)
From equation (i), the required number will be any number between 1936 and 2025. Since one part of the number is the square of 6 means one factor is 36.
∴ L, C, M of 36 and 5 = 180
∴ Number will be multiple of 180 i,e.,
180 x 11 = 1980 the only value which satisfies the equation (i).