Find an irrational number that is between 9.5 and 9.7. explain why it is irrational. include the decimal approximation of the irrational number to the nearest hundredth.

 The required number is 9.56.

Step-by-step explanation:  We are given to find an irrational number in between 9.5 and 9.7.

Also, to explain the reason behind being irrational and include the decimal approximation of the irrational number to the nearest hundredth.

We know that

a number is irrational if the digits after the decimal are non-terminating and non-repeating.

Let x be an irrational number between 9.5 and 9.7.

So, we consider that

x = 9.562536941412578914

We can see that the digits after the decimal are non-terminating and non-repeating. so, the number is irrational.

Rounding to the nearest hundredth, we get

x = 9.56.

Thus, the required number is 9.56.