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