Question

How many non perfect square numbers are there between 31^2 and 33^2?Explain your answer with reason.

Answer 1

Non perfect square numbers between 31²  & 33² = 126

Step-by-step explanation:

Numbers between

31²  & 33²

are  33²   - 31²   - 1

= (33 + 31)(33 - 31) - 1

= 64 * 2  - 1

= 128 - 1

= 127

but in between 31²  & 33²  ,  32²  would be perfect square

=> non perfect square numbers  = 127 - 1

=> non perfect square numbers between 31²  & 33² = 126

Or use formula  that 2n numbers are between n² & (n+1)²

perfect square between 31²  & 33² is 32²

numbers  between 31² & 32² = 2 * 31 = 62

numbers  between 32² & 33² = 2 * 32 = 64

non perfect Square number between 31²  & 33² =  62 + 64 = 126

Learn More:

the number of non square numbers between n square and n + 1 whole square is

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Answer 2

Answer:

Their are 127 non perfect squares between then.

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