Question

Hello, I am having difficulty with this problem, thanks. Find the smallest numberFind the largest rational numberFind the smallest irrational number

Answer 1

In order to determine which of them is the smallest number, let's convert each number into a decimal number.

`\sqrt[3]{9}=2.080083823\approx2.08`
`√(3)=1.732050808\approx1.73`
`\sqrt{(1)/(4)}=(1)/(2)=0.5`
`(-5)^(-2)=(1)/((-5)^2)=(1)/(25)=0.04`

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.