• Recognize irrational numbers in a list of numbers
• Simplify irrational numbers to their lowest terms
• Add, subtract, multiple and divide irrational numbers

Unraveling the Irrational: A Cosmic Calculation Challenge

Sam is an aspiring astronomer working on a school project to map out constellations. The project involves using measurements that often result in irrational numbers, such as distances between stars in light-years that are not whole numbers. Your task is to help Sam calculate these distances and create a scale model of a constellation.

 

Sam has a list of distances between stars, some of which are irrational. Help Sam identify which of these are irrational numbers: [latex]\sqrt{2}, \sqrt{16}, \pi, \frac{22}{7}, \sqrt{81}, \sqrt{23}[/latex].

The distance to a nearby star is [latex]10\sqrt{2}[/latex] light-years. Another star is [latex]3\sqrt{2}[/latex] light-years further than the first. What is the total distance to the second star?

Sam wonders how many times farther away the second star is compared to the distance between Earth and the Moon, which is approximately [latex]1.28\sqrt{2}[/latex] light-years.

For the scale model, Sam needs to convert the actual light-year distances into centimeters. If [latex]\sqrt{2}[/latex] light-years is represented by [latex]1[/latex] cm, what is the model distance for these two stars that is?