Question

Compare 42−−√ and 58−−√ plotted on the number line. What is the approximate difference in tenths between the two values? (1 point) Responses 58−−√ is about 1.2 greater than 42−−√ . square root of 58 is about 1.2 greater than square root of 42. 58−−√ is about 0.8 greater than 42−−√ . square root of 58 is about 0.8 greater than square root of 42. 58−−√ is about 1.8 greater than 42−−√ . square root of 58 is about 1.8 greater than square root of 42. 58−−√ is about 1.2 less than 42−−√ .

Answer 1

To compare \(\sqrt{42}\) and \(\sqrt{58}\), let's calculate their approximate values.

1. **Estimate \(\sqrt{42}\)**:
- Knowing that \(6^2 = 36\) and \(7^2 = 49\), we can estimate that \(\sqrt{42}\) is between 6 and 7.
- A closer approximation can be done:
\[
\sqrt{42} \approx 6.48 \quad (\text{by calculation or a calculator})
\]

2. **Estimate \(\sqrt{58}\)**:
- Knowing that \(7^2 = 49\) and \(8^2 = 64\), we can estimate that \(\sqrt{58}\) is between 7 and 8.
- A closer approximation can be done:
\[
\sqrt{58} \approx 7.62 \quad (\text{by calculation or a calculator})
\]

3. **Calculate the difference**:
\[
\sqrt{58} - \sqrt{42} \approx 7.62 - 6.48 = 1.14
\]

When rounding to the nearest tenth, the approximate difference is about **1.1**.

Based on the options given:

- \(\sqrt{58}\) is about **1.2 greater than** \(\sqrt{42}\).

So the closest response to this calculation would be:

**\(\sqrt{58}\) is about 1.2 greater than \(\sqrt{42}\).**