Question

find an irrirational no. between 1/7 and 2/7​

Answer 1

Answer:

Hope this answer helps the minds of children.

Answer 2

$\large\underline{\sf{Solution-}}$

➢ Irrational numbers:- Irrational numbers are those numbers whom decimal representation is non terminating nor repeating.

➢ First Method to find Irrational number between two number.

➢ Let a and b are two rational numbers, then to find an irrational number between a and b, the method is called Geometric mean method.

That means,

$\rm :\longmapsto\:An \: irrational \: number \: between \: a \: and \: b = \sqrt{ab}$

Here,

We have given two rational numbers

$\rm :\longmapsto\:a = \dfrac{1}{7}$

and

$\rm :\longmapsto\:b = \dfrac{2}{7}$

Thus,

$\rm :\longmapsto\:An \: irrational \: number \: between \: them \: is \:$

$\rm \:  =  \:  \: \sqrt{\dfrac{1}{7} \times \dfrac{2}{7} }$

$\rm \:  =  \:  \: \sqrt{\dfrac{2}{49} }$

$\rm \:  =  \:  \: \dfrac{ \sqrt{2} }{7}$

Let consider more example!!

1. Find an irrational number between 2 and 3.

The other method to find an irrational number is decimal representation.

As we know, the decimal representation of irrational numbers are non terminating and non repeating.

So,

Irrational number between 2 and 3 is 2.010010001...

2. Find an irrational number between 1/3 and 1/2

The decimal representation of 1/3 is 0.333...

and

The decimal representation of 1/2 is 0.5

So,

Irrational number between 1/3 and 1/2 is 0.404004000...