Question

find the smallest number by which 2100 must be multiplied so that the product become a perfect square find the square root of the number so obtained

Answer 1

Factor of 2100 are 2*2*5*5*3*7
Since 3 and 7 have no pair it is the required no.
7*3=21
2100*21=44100 which is the square root of 210

Answer 2

Concept: Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value. As a result, both are reverse approaches.

Given:  The number 2100

To find: Smallest number to be multiplied by 2100 and the square root of the number obtained.

Solution : Prime factors of 2100 are

2100 = 2*2*3*5*5*7

2100 = $2^2 * 3 * 5^2 *7$

Since, 3 and 7 are not in pairs, therefore the smallest number multiplied by 2100 is 3*7 = 21.

Now, 2100*21 = 44100

Therefore square root of 44100 is 210

Prime factors of 44100 are 2*2*3*3*5*5*7*7

$\sqrt{44100} = 2^2 * 3^2 * 5^2 * 7^2\\\sqrt{44100} = 2*3*5*7\\\sqrt{44100} = 210$

Hence, the smallest number by which 2100 must be multiplied so that the product becomes a perfect square is 21.

On multiplying the number obtained is 44100.

The square root of the number obtained i.e., 44100 is 210.

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