Question

Please help! Thank you in advanced!

Answer 1

An irrational number is a number that can't be written as a fraction.

√40/10 can be simplified to 4/1, so this one is rational with no doubt.

8π is irrational because pi is known to be irrational.

1/6 is a fraction itself, so it's rational.

0.3 repeating is a repeating decimal, which means it's under the category 'rational'.

I hope this helped, and if it didn't, then please leave a comment. I'm always here to explain. :)

Answer 2

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.
`\sqrt{ (40)/(10) }`

We can simplify
`(40)/(10)` to 4, since 40 ÷ 10 = 4.

From here, we are left with
`√(4)`, and since 4 is a perfect square, we can simply find our roots.


`√(4) =2`

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.
`(1)/(6)`

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
`(1)/(3)`.
Choice A is your correct answer.

And there you have it.
Hope that helped! =)