0. Irrational
,
1. Irrational
,
2. Rational
,
3. Irrational
1) Considering that Rational Numbers are the ones that can be written as ratios like:
[tex]\begin{gathered} \frac{a}{b} \\ 1,\frac{3}{2},5,\text{ }\sqrt[]{4} \end{gathered}[/tex]
2) Then we can examine each row and each expression as well. So we can begin with:
[tex]3\sqrt[]{9}\cdot\sqrt[]{2}=3\cdot3\cdot\sqrt[]{2}=9\sqrt[]{2}=12.72792\ldots[/tex]
Since the square root of 2 yields an irrational number, 9 times that yields an irrational one as well.
Irrational
[tex]\frac{\sqrt[]{9}}{\pi}=\frac{3}{\pi}=0.9452\ldots[/tex]
Note that in the second row we have an irrational number as well, a decimal and not a repeating number.
Irrational
[tex]\frac{\pi\sqrt[]{24}}{\sqrt[]{6\pi^2}}=\frac{\pi\cdot2\sqrt[]{2}\cdot\sqrt[]{3}}{\pi\sqrt[]{2}\cdot\sqrt[]{3}}=2[/tex]
Since 2 is a rational number the same as 2/1. This is a Rational one.
And Finally:
[tex]-\sqrt[]{3}+2=0.2674[/tex]
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
