Respuesta :

Answer:

[tex]B) \sqrt{2}[/tex] ÷ [tex]2\sqrt{5}[/tex]

Step-by-step explanation:

[tex]A[/tex]→ [tex]2\sqrt{5}[/tex] ÷ [tex]\sqrt{5}[/tex]

[tex]= \frac{2\sqrt{5} }{\sqrt{5} }[/tex]

2 is a rational number

[tex]B)[/tex] → [tex]\sqrt{2}[/tex] ÷ [tex]2\sqrt{5}[/tex]

[tex]=\frac{\sqrt{2} }{2\sqrt{5} }[/tex]

[tex]=\frac{\sqrt{2} }{\sqrt{2}*\sqrt{2}*\sqrt{5} }[/tex]

[tex]= \frac{1}{\sqrt{10} }[/tex]

↑ is irrational number

[tex]C)[/tex] [tex]\frac{\pi }{2}[/tex]÷ [tex]\pi[/tex]

[tex]= \frac{\pi }{2} *\frac{1}{\pi }[/tex]

[tex]=\frac{1}{2}[/tex]

↑ is a rational number

[tex]D)[/tex][tex]5\pi[/tex] ÷ [tex]\pi[/tex]

[tex]= 5[/tex]

↑ is a rational number

So, Option B is your answer

[tex]-----------------[/tex]

hope it helps..

have a great day!!!