Answer:
7
Step-by-step explanation:
Given the number: 3049200
To determine the least number by which we must divide to obtain a perfect square, we first express the number as a product of its prime factors.
3049200=2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 11 x 11
[tex]=2^4 X 3^2 X 5^2 X 7 X 11^2[/tex]
If you observe the product in exponent form, only the power of 7 is odd. Every other number is a perfect square.
Therefore, if we divide by 7, the result is a perfect square.
CHECK
[tex]\dfrac{3049200}{7} =435600\\\sqrt{435600}=660[/tex]
