Question

Find the perfect square numbers between 30 and 40 (ii) 50 and 60

Answer 1

Checking :


Number Factors
31 = 31 × 1

32 = 2 × 4²

33 = 3 × 11

34 = 2 × 17

35 = 5 × 7

36 = 2² × 3²

37 = 1 × 37

38 = 2 × 19

39 = 1 × 39





Required number = 36 = 2² × 3² = 6²

=>36




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( ii )


50 = 2 × 5²

51 = 17 × 3

52 = 2² × 13

53 = 1 × 53

54 = 6 × 3²

55 = 5 × 11

56 = 2² × 14

57 = 1 × 57

58 = 2 × 29

59 = 1 × 59




There is not satisfactory number.
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Answer 2

Checking :

Number Factors
31 = 31 × 1

32 = 2 × 4²

33 = 3 × 11

34 = 2 × 17

35 = 5 × 7

36 = 2² × 3²

37 = 1 × 37

38 = 2 × 19

39 = 1 × 39

Required number = 36 = 2² × 3² = 6²

=>36

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( ii )

50 = 2 × 5²

51 = 17 × 3

52 = 2² × 13

53 = 1 × 53

54 = 6 × 3²

55 = 5 × 11

56 = 2² × 14

57 = 1 × 57

58 = 2 × 29

59 = 1 × 59

There is not satisfactory number.

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