My apologies for the previous incomplete answer. I will now identify all irrational numbers from the full…

Question

My apologies for the previous incomplete answer. I will now identify all irrational numbers from the full list provided in the image for question 4(a).

ScanSolve AI Tutor · Accepted Answer

My apologies for the previous incomplete answer. I will now identify all irrational numbers from the full list provided in the image for question 4(a).

An irrational number is a number that cannot be expressed as a simple fraction $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \neq 0$ . Their decimal representations are non-terminating and non-repeating.

Let's examine each number from the list: $-6, -\sqrt{4}, \frac{2}{3}, \sqrt{8}, \text{ and } \pi$ .

-6
This is an integer. It can be written as $\frac{-6}{1}$ . It is a rational number.
$-\sqrt{4}$
$-\sqrt{4} = -2$
This is an integer. It can be written as $\frac{-2}{1}$ . It is a rational number.
$\frac{2}{3}$
This is already in the form of a fraction of two integers. It is a rational number.
$\sqrt{8}$
$\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$
Since $\sqrt{2}$ is an irrational number (its decimal representation is non-terminating and non-repeating), $2\sqrt{2}$ is also an irrational number.
$\pi$
This is a mathematical constant that is famously irrational. Its decimal representation is non-terminating and non-repeating. It is an irrational number.

The irrational numbers from the list are: $\sqrt{8}, \pi$

My apologies for the previous incomplete answer. I will now identify all irrational numbers from the full list provided in the image for question 4(a).

Answer

Step-by-step solution

-6

$-\sqrt{4}$

$\frac{2}{3}$

$\sqrt{8}$

$\pi$

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My apologies for the previous incomplete answer. I will now identify all irrational numbers from the full list provided in the image for question 4(a).

Answer

Step-by-step solution

-6

−4-\sqrt{4}−4​

23\frac{2}{3}32​

8\sqrt{8}8​

π\piπ

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$-\sqrt{4}$

$\frac{2}{3}$

$\sqrt{8}$

$\pi$