Question

how to find irrational number from rational and irrational numbers

Answer 1

There is no particular formula for that, we have to calculate it in our mind by converting rational numbers into decimals

Let's see an example

Let's find an irrational no. between ½ & ¼ ( between two rationals

we can calculate these fractions easily by division

we will find that

½ = 0.5 &
¼ = o.25

we find that

0.25<0.3<0.5……………eq. 1

so 0.3 is a rational no. between ½ and ¼

we can modify it to make an irrational no.

so if we write

0.31010010001…

in place of 3 in eq. 1

so we get

0.25<0.31010010001...<0.5
or
¼<0.31010010001…<½

so 0.31010010001... is an irrational no. between ½ &¼

similarly we can find many irrational no.s between 2 given rationals as well as irrationals