Question

Find the irrational number(s) lying between 2/7 and 5/9

Answer 1

Answer:

2/7 = 0.28571... and 5/9 = 0.5555... the irrational number between 2/7 and 5/9 is the irrational number between 0.28571... and 0.5555...

Answer 2

ANSWER:

The irrational number between given numbers is 0.64856…….

SOLUTION:

Given, given two numbers are  $\frac{2}{7}$ and $\frac{5}{9}$

We have to find the irrational number between above two numbers.

Now, $\frac{2}{7}=0.28571 \ldots \text { and } \frac{5}{9}=0.5555 \ldots$

So, the irrational number between $\frac{2}{7}$ and $\frac{5}{9}$ is the irrational number between 0.28571... and 0.5555...

We know that, square root of numbers other than perfect squares are irrational numbers.

So let us find the square of average of given two numbers.

Now, average of given numbers is:

$\frac{\frac{2}{2}+\frac{5}{9}}{2}=\frac{\frac{18+35}{63}}{2}=\frac{\frac{53}{63}}{2}=\frac{53}{63} \times \frac{1}{2}=\frac{53}{126}$

Now, irrational number = $\sqrt{\frac{53}{126}}=0.64856 \ldots \ldots$

Hence, one of the irrational number between given numbers is 0.64856…….