Question

Only for Genius....

Find the smallest number by which 2925 must be divided so that it becomes a perfect square also find the square root

Answer 1

Find the prime factors of 2925:

2925 = 3² x 5² x 13

Find the number:

To be a perfect square, the exponents must be in the multiple of 2s.

Let k be the number that the number needs to be divided by.

2925 = 3² x 5² x 13

Since 13 is the only number that does not have exponent that are multiple of 2s, we will take way that multiple by dividing by it.

2925/k = (3² x 5² x 13) /13

k = 13

Find the square root:

2925/13 = 3² x 5²

√3² x 5² = 3 x 5 = 15

Answer: The number is 13. The square root of the perfect square is 15