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Answer

↓Steps Explained:↓

Solve the following equation

m^2=3600

Using our radical expression calculator, we can simplify this

m² = 3600

Take the square root of each side:

√m²= √3600

m= = ±√3600

Simplify √3600

If you use a guess and check method, you see that 59² = 3481 and 61² = 3721

Since 3481 < 3600 < 3721 the next logical step would be checking 60²

60² = 60 x 60

60² = 3600 <--- We match our original number!!!

Therefore, √3600 = 60

Another method is to list out the products of integers starting at 1 as follows:

1² = 1 x 1 = 1 <--- Not our answer since 1 < 3600

2² = 2 x 2 = 4 <--- Not our answer since 4 < 3600

3² = 3 x 3 = 9 <--- Not our answer since 9 < 3600

4² = 4 x 4 = 16 <--- Not our answer since 16 < 3600

5² = 5 x 5 = 25 <--- Not our answer since 25 < 3600

6² = 6 x 6 = 36 <--- Not our answer since 36 < 3600

7² = 7 x 7 = 49 <--- Not our answer since 49 < 3600

8² = 8 x 8 = 64 <--- Not our answer since 64 < 3600

9² = 9 x 9 = 81 <--- Not our answer since 81 < 3600

10² = 10 x 10 = 100 <--- Not our answer since 100 < 3600

11² = 11 x 11 = 121 <--- Not our answer since 121 < 3600

12² = 12 x 12 = 144 <--- Not our answer since 144 < 3600

13² = 13 x 13 = 169 <--- Not our answer since 169 < 3600

14² = 14 x 14 = 196 <--- Not our answer since 196 < 3600

15² = 15 x 15 = 225 <--- Not our answer since 225 < 3600

16² = 16 x 16 = 256 <--- Not our answer since 256 < 3600

17² = 17 x 17 = 289 <--- Not our answer since 289 < 3600

18² = 18 x 18 = 324 <--- Not our answer since 324 < 3600

19² = 19 x 19 = 361 <--- Not our answer since 361 < 3600

20² = 20 x 20 = 400 <--- Not our answer since 400 < 3600

21² = 21 x 21 = 441 <--- Not our answer since 441 < 3600

22² = 22 x 22 = 484 <--- Not our answer since 484 < 3600

23² = 23 x 23 = 529 <--- Not our answer since 529 < 3600

24² = 24 x 24 = 576 <--- Not our answer since 576 < 3600

25² = 25 x 25 = 625 <--- Not our answer since 625 < 3600

26² = 26 x 26 = 676 <--- Not our answer since 676 < 3600

27² = 27 x 27 = 729 <--- Not our answer since 729 < 3600

28² = 28 x 28 = 784 <--- Not our answer since 784 < 3600

29² = 29 x 29 = 841 <--- Not our answer since 841 < 3600

30² = 30 x 30 = 900 <--- Not our answer since 900 < 3600

31² = 31 x 31 = 961 <--- Not our answer since 961 < 3600

32² = 32 x 32 = 1024 <--- Not our answer since 1024 < 3600

33² = 33 x 33 = 1089 <--- Not our answer since 1089 < 3600

34² = 34 x 34 = 1156 <--- Not our answer since 1156 < 3600

35² = 35 x 35 = 1225 <--- Not our answer since 1225 < 3600

36² = 36 x 36 = 1296 <--- Not our answer since 1296 < 3600

37² = 37 x 37 = 1369 <--- Not our answer since 1369 < 3600

38² = 38 x 38 = 1444 <--- Not our answer since 1444 < 3600

39² = 39 x 39 = 1521 <--- Not our answer since 1521 < 3600

40² = 40 x 40 = 1600 <--- Not our answer since 1600 < 3600

41² = 41 x 41 = 1681 <--- Not our answer since 1681 < 3600

42² = 42 x 42 = 1764 <--- Not our answer since 1764 < 3600

43² = 43 x 43 = 1849 <--- Not our answer since 1849 < 3600

44² = 44 x 44 = 1936 <--- Not our answer since 1936 < 3600

45² = 45 x 45 = 2025 <--- Not our answer since 2025 < 3600

46² = 46 x 46 = 2116 <--- Not our answer since 2116 < 3600

47² = 47 x 47 = 2209 <--- Not our answer since 2209 < 3600

48² = 48 x 48 = 2304 <--- Not our answer since 2304 < 3600

49² = 49 x 49 = 2401 <--- Not our answer since 2401 < 3600

50² = 50 x 50 = 2500 <--- Not our answer since 2500 < 3600

51² = 51 x 51 = 2601 <--- Not our answer since 2601 < 3600

52² = 52 x 52 = 2704 <--- Not our answer since 2704 < 3600

53² = 53 x 53 = 2809 <--- Not our answer since 2809 < 3600

54² = 54 x 54 = 2916 <--- Not our answer since 2916 < 3600

55² = 55 x 55 = 3025 <--- Not our answer since 3025 < 3600

56² = 56 x 56 = 3136 <--- Not our answer since 3136 < 3600

57² = 57 x 57 = 3249 <--- Not our answer since 3249 < 3600

58² = 58 x 58 = 3364 <--- Not our answer since 3364 < 3600

59² = 59 x 59 = 3481 <--- Not our answer since 3481 < 3600

60² = 60 x 60 = 3600 <--- This is our answer!!!

61² = 61 x 61 = 3721 <--- Not our answer since 3721 > 3600

Final Answer