Consider the number line with the plotted square roots.

Question

Inspect the number line. Which square roots have a difference of about 0.5?

(1 point)
Responses

11−−√
and 19−−√
square root of 11 and square root of 19

14−−√
and 19−−√
square root of 14 and square root of 19

19−−√
and 24−−√
square root of 19 and square root of 24

11−−√
and 14−−√

Answer 1

To find which square roots have a difference of about 0.5, we can calculate the approximate values of the square roots mentioned in the options:

1. \(\sqrt{11} \approx 3.316\)
2. \(\sqrt{14} \approx 3.742\)
3. \(\sqrt{19} \approx 4.359\)
4. \(\sqrt{24} \approx 4.899\)

Now we can calculate the differences:

• \(\sqrt{11}\) and \(\sqrt{19}\): \(\sqrt{19} - \sqrt{11} \approx 4.359 - 3.316 = 1.043\)

• \(\sqrt{14}\) and \(\sqrt{19}\): \(\sqrt{19} - \sqrt{14} \approx 4.359 - 3.742 = 0.617\)

• \(\sqrt{19}\) and \(\sqrt{24}\): \(\sqrt{24} - \sqrt{19} \approx 4.899 - 4.359 = 0.54\)

• \(\sqrt{11}\) and \(\sqrt{14}\): \(\sqrt{14} - \sqrt{11} \approx 3.742 - 3.316 = 0.426\)

From these calculations, the pairs that have a difference of about 0.5 are:

\(\sqrt{19}\) and \(\sqrt{24}\) (approx 0.54) and \(\sqrt{14}\) and \(\sqrt{19}\) (approx 0.617).

However, since you are looking for a difference that is "about 0.5", the most accurate response would be:

\(\sqrt{19}\) and \(\sqrt{24}\).

Thus, the correct answer is:

\( \sqrt{19} \text{ and } \sqrt{24} \).