Answer:
The correct number line is the third one.
Step-by-step explanation:
The picture is missing. I will attach the picture with the answer.
We need to choose the number line that correctly compares [tex]\sqrt{24}[/tex] and [tex]4.256[/tex]
First we are going to express [tex]\sqrt{24}[/tex] in decimal form ⇒
[tex]\sqrt{24}[/tex] ≅ [tex]4.8989[/tex]
We can conclude that [tex]\sqrt{24}>4.256[/tex]
Now looking at the picture in the first number line we can notice that [tex]\sqrt{24}[/tex] is placed between [tex]4.2[/tex] and [tex]4.3[/tex] which is wrong. Also we can see in the number line that [tex]4.256>\sqrt{24}[/tex] which is wrong again.
For the second number line [tex]\sqrt{24}[/tex] and [tex]4.256[/tex] are both placed incorrectly.
In the fourth number line [tex]\sqrt{24}[/tex] is placed between [tex]4.9[/tex] and [tex]5.0[/tex] which is wrong. [tex]4.256[/tex] is placed wrong between [tex]4.3[/tex] and [tex]4.4[/tex]
However the third number line is correct. [tex]\sqrt{24}[/tex] is well placed between [tex]4.8[/tex] and [tex]4.9[/tex] , [tex]4.256[/tex] is well placed between [tex]4.2[/tex] and [tex]4.3[/tex]
