Question

identify the irrational numbersselect all that apply1. 0.7292. 0.01953473. -124. $\sqrt[]{18}$

Answer 1

The options are analyzed as follows:

1: The overline 0.729 means:

$0.729729729\ldots$

This is a non- terminating recurring decimal hence it is rational.

2: The nuumber 0.0195347... is a non terminating and non recurring decimal hence it is irrational.

3. The number -12 is rational since it is an integer.

4.The number 4.565656... is a non terminating recurring decimal hence it is rational.

5. The number given by:

$\sqrt[]{18}=3\sqrt[]{2}=4.242640687\ldots$

Since square root of 2 is irrational and 3 is rational the product is irrational.

Also the decimal is non terminating non recurring hence it is irratonal.

So the options 2 and 5 are irrational.