Chapter 6.6, Problem 12OE

To determine

whether the given number is rational or irrational

Answer to Problem 12OE

It is an irrational number

Explanation of Solution

Given information :

Given number is ${\left(2\sqrt{3}\right)}^3$

Rational number are those numbers which can be represent in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$

The given number can be simplified as ${\left(2\sqrt{3}\right)}^3=24\sqrt{3}$

Hence it cannot be represented in the form $\frac{p}{q}$ with $p$ and $q$ as integers. Thus it is an irrational number.