A rational number is one which can be expressed, in its most basic form, as a fraction or whole number.
Let us take a look at our choices.
1. [tex] \sqrt{ \frac{40}{10} }[/tex]
We can simplify [tex] \frac{40}{10} [/tex] to 4, since 40 ÷ 10 = 4.
From here, we are left with [tex] \sqrt{4} [/tex], and since 4 is a perfect square, we can simply find our roots.
[tex] \sqrt{4} =2[/tex]
2 is a whole number and is therefore rational.
Choice A is your correct answer.
2. 8π
Pi in itself is an irrational number, and therefore any multiple of pi is also irrational.
Choice B is your correct answer.
3. [tex] \frac{1}{6} [/tex]
This one is already a fraction in its most basic form. Another word for a fraction IS ratio, so this is definitely a rational number.
Choice A is your correct answer.
4. 0.33...
Anytime we have a repeating decimal it is the result of a completed fraction and therefore is a rational number. In this case, 0.33... is the completed form of[tex] \frac{1}{3} [/tex].
Choice A is your correct answer.
And there you have it.
Hope that helped! =)
