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 :

$\begin{gathered} 0.23\bar{45}=0.23+0.00\bar{45} \\ =\frac{23}{100}+\frac{45}{9900}=\frac{129}{550} \end{gathered}$

So, the result will a rational number

so, the statement b is True