Expressions [tex]2\sqrt{5}-3\sqrt{5}[/tex] , [tex]\frac{\sqrt{42} }{\sqrt{68} }[/tex] and [tex]\sqrt{7}\pi-\sqrt{14}\pi[/tex] are irrational.
Expressions [tex]\frac{5\sqrt{3}-\sqrt{3} }{2\sqrt{3} }[/tex] and [tex]\frac{\sqrt{64} }{32}[/tex] are rational.
Rational and irrational expression :
The given expression are,
- [tex]2\sqrt{5}-3\sqrt{5}=\sqrt{5}(2-3)=-\sqrt{5}[/tex]
Which is irrational.
- [tex]\frac{\sqrt{42} }{\sqrt{68} }=\frac{\sqrt{42} }{2\sqrt{17} }[/tex]
Which is irrational.
- [tex]\sqrt{5}(4\sqrt{5} -3\sqrt{5} )=5[/tex]
Which is rational
- [tex]\frac{5\sqrt{3}-\sqrt{3} }{2\sqrt{3} }=2[/tex]
Which is rational.
- [tex]\frac{\sqrt{64} }{32}=\frac{8}{32}=\frac{1}{7}[/tex]
Which is rational.
- [tex]\sqrt{7}\pi-\sqrt{14}\pi=\pi(\sqrt{7}-\sqrt{14} )[/tex]
Which is irrational.
Learn more about the rational function here:
https://brainly.com/question/1851758
