Question

By what least number should 3049200 be divided to get a perfect square?

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Answer 1

7

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

`=2^4 X 3^2 X 5^2 X 7 X 11^2`

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

`(3049200)/(7) =435600\\√(435600)=660`