Question

10. Determine the validity (true or false) of the following statements and explain why.a)square root of 81is an irrational number.b) 0.2345 is a rational number.

Answer 1

At first, we should know that :

An Irrational Numbers : is a real number that cannot be written as a simple fraction.

A rational number : is a real number that can be written as a simple fraction.

So, for the option A.

`\sqrt[]{81}=9`

The number 9 is a rational number

So, the statement a is alse

For option B.

`0.23\bar{45}`

This number is the sum of :

`\begin{gathered} 0.23\bar{45}=0.23+0.00\bar{45} \\ =(23)/(100)+(45)/(9900)=(129)/(550) \end{gathered}`

So, the result will a rational number

so, the statement b is True