Question

Find the smallest whole number by which 2352 should be multiplied so as to get a perfect square number. Also find the square root of the number.​

Answer 1

to know this, we need to find the prime factorization of 2352 which is :

2 x 2 x 2 x 2 x 3 x 7 x 7 = 2352

here we can see that the number 3 is not in the pairs of 2, so 3 should be multiplied by 2352 to get a perfect square.

the new prime factorization: 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7

therefore, the square root will be :

2 x 2 x 3 x 7 = 84

this was done by taking one number of each of the pairs.

hope it helps!