Unraveling the Irrational: A Cosmic Calculation Challenge Cont.

Sam has discovered that the distances between three newly observed stars form a linear cluster. The distances from Earth to each star are as follows: Star A is [latex]\sqrt{50}[/latex] light-years away, Star B is [latex]\sqrt{50}  + \sqrt{18 }[/latex] light-years away, and Star C is [latex]\sqrt{50}  + \sqrt{18 } + \sqrt{8}[/latex] light-years away.

Sam needs to simplify these expressions to find the total light-year distances between the stars.

A star is visible from Earth when it is less than [latex]20 \sqrt{2}[/latex] light-years away, which of the stars Sam is studying will be visible?

To estimate the volume of space between the three celestial bodies, Sam multiplies their distances together. What is the approximate volume of space?

Through this series of calculations, you’ve helped Sam map out the distances between stars using irrational numbers. Your assistance has been crucial in helping Sam complete the model, showcasing the practical importance of mathematical concepts in understanding the universe.