How many non perfect square numbers are there between 31^2 and 33^2?Explain your answer with reason.
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Answered by
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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
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the number of non square numbers between n square and n + 1 whole square is
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0
Answer:
Their are 127 non perfect squares between then.
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