Question

How many rational numbers lie between 90 square and 91 square

Answer 1

Numerous numbers will come

Answer 2

Step-by-step explanation:

Given :-

90² and 91²

To find :-

How many rational numbers lie between 90² and 91² ?

Solution :-

We know that

By Densitive Property ,

There are infinitely number of many rational numbers between the two numbers.

Or for finding natural numbers which are non perfect square numbers.

We know that

The number of non perfect square numbers between n² and (n+1)² is 2n

We have , n = 90

and n+1 = 91 = 90+1

The number of non perfect square numbers

=> 2×90

=> 180

Answer :-

The number of non perfect square numbers or Natural numbers between 90² and 91² is 180

The number of rational numbers between the two numbers is Infinite.

Used formulae:-

→ Densitive Property:-

There are infinitely number of many rational numbers between the two numbers.

→ The number of non perfect square numbers between n² and (n+1)² is 2n