We want to see why the product of 2-digit numbers can't be a 2-digit number. This is because the product of two 2-digit numbers is always a 3-digit or 4-digit number.
First, remember that any 2-digit number can be written as:
10k
Where 1 ≤ k < 10
to give some examples:
- 10 = 101
- 33 = 103.3
- 98 = 109.8
Then two 2-digit numbers A and B can be written as:
A = 10k
B = 10k'
Then the product of these two numbers is:
AB = (10k)(10k') = (1010)(kk') = 100(kk´)
So we can see that the product of two 2-digit numbers is always equal to or larger than 100 (this happens because 100 > kk' ≥ 1)
So the product of two 2-digit numbers is always a 3-digit or 4-digit number, this is why it can't be a 2-digit number.
If you want to learn more, you can read:
https://brainly.com/question/6073907
