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Question

There are _________ natural numbers between n2 and (n+1)2.


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Solution

Explanation:

Lets take any two consecutive natural numbers n=2 and n+1=2+1=3.

n2=22=2×2=4 and

n+12=32=3×3=9

Therefore, Natural numbers between the squares of 2 and 3 are 5,6,7,8 which are 2×n=2×2=4 numbers.

Lets take any other two consecutive natural numbers n=5 and n+1=5+1=6.

n2=52=5×5=25 and

n+12=62=6×6=36

Therefore, Natural numbers between the squares of 5 and 6 are 26,27,28,29,30,31,32,33,34,35 which are 2×n=2×5=10 numbers.

Therefore, there are 2n natural numbers between n2 and (n+1)2.


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