Question

State an irrational number lying between 2/5 and 3/7

​

Answer 1

Answer:

first we divide both

2/5=0.40..

3/7=0.42..

the irrational number lying are 0.401400140001..

Answer 2

Answer:

$\sqrt{\frac{6}{35} }$ is an irrational number lying between 2/3 and 3/7

Step-by-step explanation:

Between any two rational number, there exists infinite number of irrationals.

Irrational number: The number which cannot be written in the p/q form, q≠0, where p and q are integers.

Generally, irrational numbers are non-repeating, non-terminating decimals.

Step 1 of 2

To find: An irrational number between 2/5 and 3/7.

Since the product of the numbers 2/5 and 3/7 is,

⇒ $\frac{2}{5} \times\frac{3}{7}$

⇒ $\frac{6}{35}$

⇒ $0.1714285714\ .\ .\ .$

Notice that the number is non-terminating but repeating decimal.

Step 2 of 2

Take square root of the number 6/35 as follows:

⇒ $\sqrt{\frac{6}{35} }$

⇒ $0.414039335\ .\ .\ .$

Clearly, the number is non-repeating, non-terminating decimal.

Thus, the number $\sqrt{\frac{6}{35} }$ is an irrational number lying between 2/3 and 3/7.

#SPJ2