Answer:
(a)
[tex]\sqrt{105} => Irrational[/tex]
[tex]-4 => Integer[/tex]
[tex]\frac{4}{3} => Rational[/tex]
(b)
[tex]-4[/tex] [tex]\frac{4}{3}[/tex] [tex]\sqrt{105}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{105}[/tex]
[tex]-4[/tex]
[tex]\frac{4}{3}[/tex]
Solving (a): The category of number the belong to
[tex]\sqrt{105}[/tex]
Solve the square root
[tex]\sqrt{105} = 10.246950766[/tex]
The result is irrational;
So:
[tex]\sqrt{105} => Irrational[/tex]
[tex]-4 => Integer[/tex]
[tex]\frac{4}{3}[/tex]
This has an integer numerator and denominator;
So:
[tex]\frac{4}{3} => Rational[/tex]
Solving (b): Order from least to greatest
i. [tex]\sqrt{105} = 10.246950766[/tex]
ii. [tex]-4[/tex]
iii. [tex]\frac{4}{3} = 1.33333[/tex]
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:
[tex]-4[/tex] [tex]\frac{4}{3}[/tex] [tex]\sqrt{105}[/tex]
