How many numbers lie between squares of the following numbers? (i) 12 and 13

(ii) 25 and 26

(iii) 99 and 100

Solution :

The numbers between n^2n

2

and (n+1)^2(n+1)

2

there are 2n non-square numbers.

(i) 12 and 13

i.e. n=12

So, between 12^212

2

and 13^213

2

There are 2\times 12=242×12=24 numbers.

(ii) 25 and 26

i.e. n=25

So, between 25^225

2

and 26^226

2

There are 2\times 25=502×25=50 numbers.

(iii) 99 and 100

i.e. n=99

So, between 99^299

2

and 100^2100

2

There are 2\times 99=1982×99=198 numbers.

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