Find the smallest number by which 4851 must be multiplied so that the product becomes a perfect square.

To do:

We have to find the smallest number by which 4851 must be multiplied so that the product becomes a perfect square.

Solution:

Perfect Square: A perfect square has each distinct prime factor occurring an even number of times.

$4851=3\times3\times7\times7\times11$

$=(3)^2\times(7)^2\times11$

$4851\times11=(3)^2\times(7)^2\times11\times11$

$=(3\times7\times11)^2$

$=(231)^2$

In order to make the pairs an even number of pairs, we have to multiply 4851 by 11, then the product will be the perfect square.

Therefore, 11 is the smallest number by which 4851 must be multiplied so that the product is a perfect square.

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Updated on: 10-Oct-2022

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