The small squares on a chessboard can be combined to form larger squares. For example, there are sixty-four 1x1 squares and one 8x8 square. Use inductive reasoning to determine how many 2x2 squares, 3x3 squares, and so on, are on a chessboard. What is the total number of squares on a chessboard?

204

Step-by-step explanation:

Given that a 1x1 square can be located in 8 places horizontally and 8 places vertically,

Then we have 1x1 squares: 8² = 64

Again the subsequent squares will be written as

2x2 squares: 7² (2 squares in 7 places both horizontal and verticals) = 49

3x3 squares: 6² (3 squares in 6 places both horizontal and verticals)= 36

4x4 squares: 5² (4 squares in 5 places both horizontal and verticals)= 25

5x5 squares: 4² (5 squares in 4 places both horizontal and verticals)= 16

6x6 squares: 3² (6 squares in 3 places both horizontal and verticals)= 9

7x7 squares: 2² (7 squares in 2 places both horizontal and verticals)= 4

8x8 squares: 1² (8 squares in 1 places both horizontal and verticals)= 1

Hence, the total number of squares on chessboard is 1+4+9+16+25+36+49+64 = 204.

204

Step-by-step explanation:

need more answers? just follow me

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above