Question

between 18² and 19² how many natural number are there ( a ) 38 ( b ) 36 (c) 42 (d) 40​

Answer 1

Answer:

36 natural numbers lie between 18 squared and 19 squared.

Step-by-step explanation:

To find : How many natural numbers lie between 18 square and 19 square?

Solution :

The square of numbers is

18^2 = 32418

2

=324

19^2 = 36119

2

=361

The natural numbers between 18^218

2

and 19^219

2

are the numbers in the sequence

325, 326,…….., 359, 360 this form an A.P

Where, first term is a=325

Common difference is d=1

Last term is l=360

Using last term formula,

l=a+(n-1)dl=a+(n−1)d

360=325+(n-1)1360=325+(n−1)1

n-1=360-325n−1=360−325

n-1=35n−1=35

n=36n=36

Therefore, 36 natural numbers lie between 18 squared and 19 squared.

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Answer 2

Answer:

36 natural numbers

Step-by-step explanation:

Number of natural numbers lying between n² and (n+1)²

=(n+1)²−n² −1=2n

Therefore, the number of natural numbers lying between 18²

and 19²

=2n=2×18=36 numbers.