Question

find the smallest no by which 17640 is multiplied so that product is perfect square

Answer 1

Solution:-
LCM of 17640=
$2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7 \times 7$
Here,we can see that prime factor 2,3,7 are in pair but 5 and 2 is not in pair.

For a number to be a perfect square ,its prime factor should by in pair.

So,in order to make 17640 a perfect square we need to make 5 and 2 also in pair.

5×2=10

So,the smallest number by which 17640 should be multiplied to make it perfect square is 10.

Answer 2

Hello

Here is the answer for your question

First we will do the prime factorization of 17640 to get the factored of 17640

17640= 2×2×2×3×3×5×7×7
Now we will make the pairs
Here 2 and 5 are unpaired so to make them paired .

We will multiply by 2× 5= 10

Then all the factors will be paired and it will become the perfect square of 420


Hence , the answer is 10


Hope it helps

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