In order to determine which of them is the smallest number, let's convert each number into a decimal number.
[tex]\sqrt[3]{9}=2.080083823\approx2.08[/tex][tex]\sqrt{3}=1.732050808\approx1.73[/tex][tex]\sqrt{\frac{1}{4}}=\frac{1}{2}=0.5[/tex][tex](-5)^{-2}=\frac{1}{(-5)^2}=\frac{1}{25}=0.04[/tex]
Upon converting, we can easily that the smallest number is the fourth number which is (-5)^-2.
On the other hand, between the 4 numbers, there are only two rational numbers and these are the 3rd and the 4th number. Between the two, the largest rational number is the 3rd number which is √(1/4) equivalent to 0.5.
Lastly, between the 4 numbers, there are only two irrational numbers and these are the first and the second number. Between the two, the smallest irrational number is √3 which is equivalent to 1.73.
