Using rational approximations, what is an inequality statement comparing [tex]\sqrt{21}[/tex] and [tex]\sqrt{17}[/tex]?

Enter <, >, or [tex]=[/tex].

The inequality is: [tex]\sqrt{21} \square \sqrt{17}[/tex].



Answer :

To compare [tex]\(\sqrt{21}\)[/tex] and [tex]\(\sqrt{17}\)[/tex] using rational approximations, we first need to understand the values of these square roots.

The approximate value of [tex]\(\sqrt{21}\)[/tex] is around 4.5826 and [tex]\(\sqrt{17}\)[/tex] is around 4.1231.

Step-by-step comparison:
1. Determine the value of [tex]\(\sqrt{21}\)[/tex]:
[tex]\[ \sqrt{21} \approx 4.5826 \][/tex]

2. Determine the value of [tex]\(\sqrt{17}\)[/tex]:
[tex]\[ \sqrt{17} \approx 4.1231 \][/tex]

3. Compare the two values:
[tex]\[ 4.5826 \quad \text{and} \quad 4.1231 \][/tex]

Since 4.5826 is greater than 4.1231, we can state the inequality as:
[tex]\[ \sqrt{21} > \sqrt{17} \][/tex]

Thus, the inequality is:
[tex]\[ \sqrt{21} > \sqrt{17} \][/tex]