Question

By what least number should we multiply 8400, so that it becomes a perfect square?

Answer 1

we have to multiply it by 3*7 i.e. 21 to make it a perfect square.

Answer 2

The least number is 21

Given,

According to the question the given number is 8400

To Find,

We have To Find the least number should we multiply 8400, so that it becomes a perfect square?

Solution,

If we are multiple the number to find the given number 8400

then we find that,

8400= 2*2*2*2*5*5*3*7 ...........(i)

from equation 1 we say that

8400= 2²*2²*5²*3*7

Now, if we are multiplying 21 with the given number 8400

then the result is : 8400*21= 176400

similarly in this case we find the multiplication of 176400

so, 176400= 2*2*2*2*5*5*3*3*7*7

or, 176400= 2² * 2²* 3² * 5² * 7²

so, 176400= (420)² ..................(ii)

We can find that 176400 is perfect square of 420.

Hence, the least number is 21, that we should multiply 8400, so that it becomes a perfect square.

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