Answer:
- The given number is irrational.
Step-by-step explanation:
It is known that [tex]\sqrt{2}[/tex] is irrational.
Given number can be converted as:
- [tex]5\sqrt{32} =[/tex]
- [tex]5\sqrt{16*2} =[/tex]
- [tex]5\sqrt{16}*\sqrt{2} =[/tex]
- [tex]5*4*\sqrt{2} =[/tex]
- [tex]20\sqrt{2}[/tex]
Since [tex]\sqrt{2}[/tex] is irrational, [tex]20\sqrt{2}[/tex] is also irrational (the product of an irrational number and a rational number is irrational), so the given number is irrational.
