Sec 101 19 How many of the numbers from 10 through 83 have t

Sec. 10.1, #19

How many of the numbers from 10 through 83 have the sum of their digits equal to a perfect square?

There are ______ numbers whose digits sum to a perfect square.

The numbers starts form 10,11,12,....83.

10=1+0=1 which is a perfect square

1+3=4

2+2=4

3+1=4

4+0=4

thera are 4 numbers(13,22,31,40) whose sum is a perfect square.

1+8=9

2+7=9

3+6=9

4+5=9

5+4=9

6+3=9

7+2=9

8+1=9

9 is a perfect sq and there are 8 no in total whose sum=9 and it is a perfect square.

7+9=16

16 is a perfect sq and can be with 79 no only

There are 14 no in total whose digits sum to a perfect square.