Question

Can you help me i don’t know the answers

Answer 1

yeah i agree

root 2
pi
root 3

root 20 over 5

11/4

Answer 2

1)

An irrational number is a number that a) can't be written as a fraction of two whole numbers AND b) is an infinite decimal without any sort of pattern.

For the first answer choice, clearly
`(1)/(3)` does not pass the first criterion so we look at the second choice.

Let's come back to
`√(2)` and
`\pi`.


`(2)/(9)` doesn't meet our first criterion, and let's skip
`√(3)` for now.

It is often easier to disprove an irrational number than to prove one. There are a few famous irrationals to know (although there is an infinite number of irrationals). The most common are
`√(2), \pi, e, √(3)`. For now, it's just helpful to know these and recognize them.

So we can check off
`√(2), \pi` and
`√(3)`.

2)

For this next question, we know that
`√(64) = 8`. Clearly this isn't irrational. Likewise,
`(1)/(2)` isn't irrational.
`(16)/(4) = (4)/(4) = 1`, which is rational, leaving only
`( √(20))/(5) = (2 √(5) )/(5)`. By process of elimination, this is the correct answer. Indeed,
`√(5)` is an irrational number.

3) This notation means that we have 0.3636363636... and so on, to an infinite number of digits. It is called a repeating decimal.

But it can be written as a fraction because its pattern repeats, unlike for an irrational number.

Let's say
`x=0.36363636...`. Would you agree that
`100x=36.36363636...`? (We choose to multiply by 100 because there are two decimals that repeat. For 1, choose 10, for 3 choose 1,000, and so on.)

Now, let's subtract x from 100x and solve.


`100x=36.36363636\\-x \ \ \ \ \ \ \ -0.36363636\\99x=36\\\\x= (36)/(99)= (4)/(11)`

Voila!