Compare 42−−√

Question

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 less than 42−−√
.
square root of 58 is about 1.2 less 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 greater than 42−−√
.

Answer 1

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

1. Estimate \(\sqrt{42}\):

   • We know \(6^2 = 36\) and \(7^2 = 49\), so \(\sqrt{42}\) is between 6 and 7.
   • A more precise calculation yields: \(\sqrt{42} \approx 6.48\).

2. Estimate \(\sqrt{58}\):

   • We know \(7^2 = 49\) and \(8^2 = 64\), so \(\sqrt{58}\) is between 7 and 8.
   • A more precise calculation yields: \(\sqrt{58} \approx 7.62\).

Now we can calculate the difference:

\[ \sqrt{58} - \sqrt{42} \approx 7.62 - 6.48 \approx 1.14. \]

When rounding to the nearest tenth, this difference is approximately 1.1.

From the given options:

• "58−−√ is about 1.2 greater than 42−−√." is the closest response as it indicates that \(\sqrt{58}\) is greater than \(\sqrt{42}\).

Thus, the correct response is:

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