What is the sum of squares of the digits from 1 to 10?

The sum of the squares of the digits from 1 to 10 is 385.

Calculation Breakdown

Here's how we arrive at that answer:

1. List the numbers: We are looking at the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
2. Square each number:
   • 1² = 1
   • 2² = 4
   • 3² = 9
   • 4² = 16
   • 5² = 25
   • 6² = 36
   • 7² = 49
   • 8² = 64
   • 9² = 81
   • 10² = 100
3. Sum the squares: 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385

Formulaic Approach

A more general approach involves a formula for the sum of the squares of the first n natural numbers:

Sum = n(n+1)(2n+1) / 6

In our case, n = 10, so:

Sum = 10(10+1)(2*10+1) / 6
Sum = 10(11)(21) / 6
Sum = 2310 / 6
Sum = 385

Conclusion

Therefore, the sum of the squares of the numbers from 1 to 10 is indeed 385.