Question

find the smallest natural number by which 1200 should be multiplied so that the square root of the product is a rational number

Answer 1

Prime factorization of 1200 = 2 * 2 * 2 * 2 * 3 * 5 * 5

As the prime factor 3 has no pair, 1200 is not a perfect square.If 3 gets a pair, then the number will be a perfect square.

So, 1200 * 3 = 3600(60 - which is a perfect square).


Hence the required smallest number is 3.


Hope this helps!

Answer 2

Prime Factorisation of 1200 =
$2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5$
Once we group them ( into 2's ) 3 remains . . .

Therefore, 1200 should be multiplied with 3 which gives=
$1200 \times 3 = 3600$
$\sqrt{3600 } = 60$
Therefore the Smallest Number is 3 that must be multiplied to make 1200 a perfect square.