Question

Compare √7 and √12 plotted on the number line. What is the approximate difference in tenths between the two values?

A number line going from 0 to 4. Points StartRoot 7 EndRoot and StartRoot 12 EndRoot are plotted.

 

StartRoot 12 EndRoot is
greater thanStartRoot 7 EndRoot.

Answer 1

To compare \(\sqrt{7}\) and \(\sqrt{12}\), we can approximate their values.

1. **Calculate \(\sqrt{7}\)**:
- We know that \(2.5^2 = 6.25\) and \(2.6^2 = 6.76\) and \(2.7^2 = 7.29\).
- Therefore, \(\sqrt{7} \approx 2.645\).

2. **Calculate \(\sqrt{12}\)**:
- We know that \(3.4^2 = 11.56\) and \(3.5^2 = 12.25\).
- Therefore, \(\sqrt{12} \approx 3.464\).

Now we can compare these two values:
- \(\sqrt{7} \approx 2.645\)
- \(\sqrt{12} \approx 3.464\)

Next, we find the approximate difference between \(\sqrt{12}\) and \(\sqrt{7}\):

\[
\sqrt{12} - \sqrt{7} \approx 3.464 - 2.645 = 0.819
\]

Rounding \(0.819\) to the nearest tenth gives:
- The difference is approximately \(0.8\).

Therefore, on the number line, \(\sqrt{12}\) is greater than \(\sqrt{7}\) and the approximate difference in tenths between the two values is **0.8**.