Question

Name the subset(s) of real numbers to which each number belongs. Then order the numbers from least to greatest. 105−−−√,−4,43

Answer 1

(a)

`√(105) => Irrational`

`-4 => Integer`

`(4)/(3) => Rational`

(b)

`-4`
`(4)/(3)`
`√(105)`

Explanation:

Given

`√(105)`

`-4`

`(4)/(3)`

Solving (a): The category of number the belong to

`√(105)`

Solve the square root

`√(105) = 10.246950766`

The result is irrational;

So:

`√(105) => Irrational`

`-4 => Integer`

`(4)/(3)`

This has an integer numerator and denominator;

So:

`(4)/(3) => Rational`

Solving (b): Order from least to greatest

i.
`√(105) = 10.246950766`

ii.
`-4`

iii.
`(4)/(3) = 1.33333`

List out the corresponding numbers:

10.246950766; -4 and 1.333333

Reorder: from least to greatest:

-4; -1.3333333 and 10.246950766

Hence; The correct order is:

`-4`
`(4)/(3)`
`√(105)`