A rational number between √2 and √3 is? please send step by step explanation.
Answers
Given : Two irrational numbers √2 and √3
To find : A rational number between these two
Solution :
A rational number is one which has either a terminating or a non terminating but recurring decimal expansion.
and we know that a rational number is one which can be expressed as the ratio of two Integers such as p/q where q is a non zero integer as division by 0 is not defined.
Value of √3 is something 1.732...
Value of √2 is something 1.414...
We have to find out a number between 1.414... and 1.732... whose decimal expansion is either terminating or non terminating but repeating.
1.3 can be eligible whose decimal expansion is terminating.
Hence the required answer is 1.3.
Remember that,
There are infinite rational numbers between two irrational numbers.
More :-
π ( pi ) a constant is an irrational number whose decimal expansion is non terminating non repeating.
There is no exact value of π but it is taken approximately 22/7. In real it has infinite number of decimal places.
π = 3.14159265. . .