Question

find the smallest number by which 2400 must be divided , so that the quotient becomes a perfect square . also find the square root of the perfect square​

Answer 1

Answer:

Solution:-

Prime factorization of 2400

2 |2400

|_________

2 |1200

|_________

2 | 600

|_________

2 | 300

|_________

2 | 150

|_________

3 | 75

|_________

5 | 25

|_________

5 | 5

|_________

| 1

|

2400 = 2*2*2*2*2*3*5*5

There are one 2 and one 3 in the above which are without any pair.

Therefore, the smallest number is 2*3 = 6, by which 2400 is to be multiplied to get a perfect square.

Resulting number = 2400*6 = 14400

Square root of 14400

120

___________

1 |14400

|1

|_____

22 |044

| 44

|______

| 000

|______

Hence, √14400 = 120