Question

Find the least number by which 31752 must be divided so as to get a perfect
square. Also find the square root of the resulting number.

Answer 1

Step-by-step explanation:

Hence 5 is the least number by which 13720 must be divided so that the quotient ia a perfect square. please mark my answer as brainleist

Answer 2

Step-by-step explanation:

Solution :-

To find the least number by 31752 should be

divided so that the resulting

number becomes a perfect square, we have to find the prime factorization of 31752

Prime factorization of 31752

2 | 31752

|_____

2 | 15876

|_____

2 |7938

|_____

3 |3969

|_____

3 |1323

|_____

3 |441

|_____

3 |147

|______

7 |49

|______

7 |7

|______

7 |1

Prime factorization of 31752 2 x 2 x 2 x 3 x 3 x 3 x 3 x 7 x 7 x 7

We can see that only 2 and 7 are unpaired.

So, 2 x 7 = 14, is the least number should be divided so that the resulting

number is a perfect square.

Let us check it.

31752 - 14 = 2268

√2268 = 47

Hence proved.