Answer :

When adding the numbers 172 and 264, regrouping is necessary because of the sum of the digits in a specific place value.

Here's why:

1. Adding the Ones Place:
- Look at the ones digits: 2 (from 172) and 4 (from 264).
- When you add these together, 2 + 4 = 6.
- Since the result is less than 10, there's no need to regroup in the ones place.

2. Adding the Tens Place:
- Look at the tens digits: 7 (from 172) and 6 (from 264).
- Adding these gives you 7 + 6 = 13.
- Since 13 is larger than 9, you need to regroup. The 3 stays in the tens place of the result, and the 1 is carried over to the hundreds place.

3. Adding the Hundreds Place:
- Look at the hundreds digits: 1 (from 172) and 2 (from 264).
- Initially, adding these gives 1 + 2 = 3.
- Don't forget the 1 carried over from the tens place, so add that to get 3 + 1 = 4.

Finally, combine everything:
- In the ones place, you have a 6.
- In the tens place, you have a 3 (from the regrouped result).
- In the hundreds place, you have a 4.

The final result is 436. So, regrouping was necessary in the tens place due to the overflow of the sum exceeding 9.

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