Question

Can you help me i don’t know the answers

Answer 1

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 $\frac{1}{3}$ does not pass the first criterion so we look at the second choice.

Let's come back to $\sqrt{2}$ and $\pi$.

$\frac{2}{9}$ doesn't meet our first criterion, and let's skip $\sqrt{3}$ 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 $\sqrt{2}, \pi, e, \sqrt{3}$. For now, it's just helpful to know these and recognize them.

So we can check off $\sqrt{2}, \pi$ and $\sqrt{3}$.

2) 

For this next question, we know that $\sqrt{64} = 8$. Clearly this isn't irrational. Likewise, $\frac{1}{2}$ isn't irrational. $\frac{16}{4} = \frac{4}{4} = 1$, which is rational, leaving only $\frac{ \sqrt{20}}{5} = \frac{2 \sqrt{5} }{5}$. By process of elimination, this is the correct answer. Indeed, $\sqrt{5}$ 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.

$100x=36.36363636\\-x \ \ \ \ \ \ \ -0.36363636\\99x=36\\\\x= \dfrac{36}{99}= \dfrac{4}{11}$

Voila!

Answer 2

Yeah i agree

root 2 
pi
root 3

root 20 over 5

11/4