Question

a.how many natural numbers are there between square of 12 and 13? b. how many natural numbers are there between square of 24 and 25 ?

Answer 1

Answer:

a.The number of non square numbers

    between n² and ( n + 1 )² is 2n

Here ,

n = 12 ,

n + 1 = 13

Therefore ,

Number of natural numbers lie  between 12² and 13² = 2 × 12

                                                                                        = 24

b. 24 and 25 are consecutive terms so 24 can be n

    n^2+(n+1)^2=2n

     n=24

So no. of terms present between 24^2 and 25^2=48.

Hope it helps you.

Answer 2

a.

square of 12=144

square of 13=169

therefore the no. of natural numbers between them = 169-144-1

                                                                                       =24

b.

square of 24=576

square of 25=625

therefore the no. of natural numbers between them =625-576-1

                                                                                       =48

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