Join IDNLearn.com today and start getting the answers you've been searching for. Discover prompt and accurate answers from our community of experienced professionals.
Sagot :
To determine where [tex]\(\sqrt{24}\)[/tex] would be plotted on the number line, we start by identifying between which two consecutive integers [tex]\(\sqrt{24}\)[/tex] lies.
First, we approximate the value of [tex]\(\sqrt{24}\)[/tex]. We find that:
[tex]\[ \sqrt{24} \approx 4.898979485566356 \][/tex]
Next, we need to determine the two integers between which this value falls. Clearly, [tex]\(\sqrt{24}\)[/tex] is greater than 4 and less than 5, as [tex]\(4.898979485566356\)[/tex] lies between 4 and 5.
Now, to establish whether [tex]\(\sqrt{24}\)[/tex] is closer to 4 or to 5, we can compare it with the midpoint between 4 and 5. This midpoint is calculated as follows:
[tex]\[ \text{Midpoint} = \frac{4 + 5}{2} = 4.5 \][/tex]
Next, we compare the value of [tex]\(\sqrt{24}\)[/tex] with the midpoint:
[tex]\[ 4.898979485566356 \, > \, 4.5 \][/tex]
Since [tex]\(4.898979485566356\)[/tex] is greater than 4.5, it means [tex]\(\sqrt{24}\)[/tex] is closer to 5 than to 4.
Therefore, [tex]\(\sqrt{24}\)[/tex] would be plotted on the number line:
Between 4 and 5, but closer to 5.
First, we approximate the value of [tex]\(\sqrt{24}\)[/tex]. We find that:
[tex]\[ \sqrt{24} \approx 4.898979485566356 \][/tex]
Next, we need to determine the two integers between which this value falls. Clearly, [tex]\(\sqrt{24}\)[/tex] is greater than 4 and less than 5, as [tex]\(4.898979485566356\)[/tex] lies between 4 and 5.
Now, to establish whether [tex]\(\sqrt{24}\)[/tex] is closer to 4 or to 5, we can compare it with the midpoint between 4 and 5. This midpoint is calculated as follows:
[tex]\[ \text{Midpoint} = \frac{4 + 5}{2} = 4.5 \][/tex]
Next, we compare the value of [tex]\(\sqrt{24}\)[/tex] with the midpoint:
[tex]\[ 4.898979485566356 \, > \, 4.5 \][/tex]
Since [tex]\(4.898979485566356\)[/tex] is greater than 4.5, it means [tex]\(\sqrt{24}\)[/tex] is closer to 5 than to 4.
Therefore, [tex]\(\sqrt{24}\)[/tex] would be plotted on the number line:
Between 4 and 5, but closer to 5.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.