Question

Hi, can you help me to solve and explain to me how to find the results please!

Answer 1

0. Irrational

,

1. Irrational

,

2. Rational

,

3. Irrational

1) Considering that Rational Numbers are the ones that can be written as ratios like:

`\begin{gathered} (a)/(b) \\ 1,(3)/(2),5,\text{ }\sqrt[]{4} \end{gathered}`

2) Then we can examine each row and each expression as well. So we can begin with:

`3\sqrt[]{9}\cdot\sqrt[]{2}=3\cdot3\cdot\sqrt[]{2}=9\sqrt[]{2}=12.72792\ldots`

Since the square root of 2 yields an irrational number, 9 times that yields an irrational one as well.

Irrational

`\frac{\sqrt[]{9}}{\pi}=(3)/(\pi)=0.9452\ldots`

Note that in the second row we have an irrational number as well, a decimal and not a repeating number.

Irrational

`\frac{\pi\sqrt[]{24}}{\sqrt[]{6\pi^2}}=\frac{\pi\cdot2\sqrt[]{2}\cdot\sqrt[]{3}}{\pi\sqrt[]{2}\cdot\sqrt[]{3}}=2`

Since 2 is a rational number the same as 2/1. This is a Rational one.

And Finally:

`-\sqrt[]{3}+2=0.2674`

Notice that the square root of 3 is already irrational so the sum of that with 2 yields another irrational number.

Irrational

3) Hence, the answer is:

0. Irrational

,

1. Irrational

,

2. Rational

,

3. Irrational