To compare [tex]\(\sqrt{18}\)[/tex] and [tex]\(\frac{23}{5}\)[/tex], let’s proceed with the calculations step-by-step.
1. Calculating [tex]\(\sqrt{18}\)[/tex]:
The square root of 18 can be determined. The value of [tex]\(\sqrt{18}\)[/tex] is approximately:
[tex]\[
\sqrt{18} \approx 4.242640687119285
\][/tex]
2. Calculating [tex]\(\frac{23}{5}\)[/tex]:
Next, we divide 23 by 5. The value of [tex]\(\frac{23}{5}\)[/tex] is:
[tex]\[
\frac{23}{5} = 4.6
\][/tex]
3. Comparing [tex]\(\sqrt{18}\)[/tex] and [tex]\(\frac{23}{5}\)[/tex]:
We now compare the two values obtained:
[tex]\[
4.242640687119285 \quad \text{and} \quad 4.6
\][/tex]
Clearly, [tex]\(4.242640687119285 < 4.6\)[/tex].
Therefore, [tex]\(\sqrt{18} < \frac{23}{5}\)[/tex].
Thus, the correct comparison is:
[tex]\[
\sqrt{18} < \frac{23}{5}
\][/tex]
