Beta is a real number

0 < Beta < 1

F = square root of ( 1 - Beta Squared / ( 1 + Beta Squared ) )

Name at least one rational number value of Beta that gives me a rational number value for F

Equation for special relativity longitudinal doppler shift with object moving away at speed V where Beta = V / C

If my formula is wrong let me know

I want to find one or more numbers that are easy to use without a calculator for an examp!e problem or example problems

I will not give you credit

If Beta = 4/5 = 0.8

Then 1 - Beta^2 = 0.36

The square root of 0.36 = 0.6 which is a rational number

But
1 + Beta^2 = 16/25 + 25/25 = 41/25

The square root of 41/25 is not a rational number

The square root of a rational number times an irrational number is an irrational number

the recripical of an irrational number is an irrational number

the product of two irrational numbers is an irrational number

the product of two rational numbers is a rational number

So 4/5 does not work for Beta

@shortstories "the product of two irrational numbers is an irrational number"
false. take a = 2 ↑ (1 ÷ 3), b = 2 ↑ (2 ÷ 3)
a ∉ ℚ ∧ b ∉ ℚ ∧ a · b ∈ ℚ