what must subtract from 99 to make it a perfect square

Question

what must subtract from 99 to make it a perfect square by prime factorization method

 

Answer 1

The list of perfect squares

 

1*1 = 1

2*2 = 4

3*3 = 9

4*4 = 16

5*5 = 25

6*6 = 36

7*7 = 49

8*8 = 64

9*9 = 81

 

Now 10*10 = 100 which is larger than 99 so that's too large to be a candidate for this problem.  

 

let's take a case of 1*1 = 1

In order to make 99 into 1, you subtract 98.  

So one of the answers is 98.

 

In the same fashion, you do 

 

99 - 98 = 1 (=1*1)

99 - 95 = 4 (=2*2)

99 - 90 = 9 (=3*3)

 

I think you can do the rest.  The answers are 98, 95, 90 and so on.

 

 

Wish you best

Mitsuko