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

Factories 1200 by factor method.
1200=2x2x5x5x2x2x3
so three is the smallest natural number by which 1 200 should be multiplied so that the square root of the product is a rational number.
1200X 3=3600

Answer 2

Answer: 3 is the smallest natural number by which 1200 should be multiplied so that to make it a perfect square.

Step-by-step explanation:

We have 1200,

We first factorise the number "1200":

$1200=2\times 2\times 2\times 2\times \times 3\times 5\times 5$

We can see that 3 has no pair.

To make it a perfect square, we will multiply by 3 on both the sides.

$1200\times 3=2\times 2\times 2\times 2\times 3\times 3\times 5\times 5\\\\\sqrt{3600}=\sqrt{2\times 2\times 2\times 2\times 3\times 3\times 5\times 5}\\\\\sqrt{3600}=2\times 2\times 3\times 5\\\\\sqrt{3600}=60$

Hence, 3 is the smallest natural number by which 1200 should be multiplied so that to make it a perfect square.