Question

how can we find this

question is.. classify the following numbers as rational or irrational

explain this step by step​

Answer 1

Ok..

Here is what you want!

i. √23 = 4.795831...

Here, firstly you need to know how to convert √23 into a decimal number. You can find this in the attachment above.

It is some sort of Division.

$\purple{after \: finding \: the \: decimal \: expansion.. \: you \: need \: to \: observe \: the \: decimal \: expansion \: whether \: the \: expansion \: is \: terminating \: or \: non - \: terminating \: or \: repeating \: or \: not. }$

Here is the example of a repeating decimal expansion:

0.1212121212....

25.253425342534..

Here is the example of a Terminating decimal expansion:

1.2571

2.576

In the above two examples.. the decimal expansion is terminating in the sense it is ending.

Here is the example of a Non - terminating decimal expansion:

1.238939937479297366392662497389..........

56.8479294875939388....

1.01001000100001....

In the above two examples.. the decimal expansion is non - terminating in the sense it is never ending decimal expansion.

So after classifying it into terminating decimal expansion or non - terminating or repeating, you need to follow the below steps..

If the decimal expansion is non - terminating and repeating it is a rational number or in other words, it can be written in the form of p/q where q ≠ 0.

If the decimal expansion is terminating then it is a rational number.

If the decimal expansion is non - termination and non - repeating then it is an irrational number.

Now hope u got what was explained☺️.