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

58−−√
is about 1.2 greater than 42−−√
.

Answer 1

To find the approximate difference between \(\sqrt{42}\) and \(\sqrt{58}\), we can first estimate the values of the square roots:

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

   • Since \(6^2 = 36\) and \(7^2 = 49\), \(\sqrt{42}\) is between 6 and 7.
   • A more precise estimate: \(\sqrt{42} \approx 6.48\).

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

   • Since \(7^2 = 49\) and \(8^2 = 64\), \(\sqrt{58}\) is between 7 and 8.
   • A more precise estimate: \(\sqrt{58} \approx 7.62\).

Now, we can calculate the difference: \[ \sqrt{58} - \sqrt{42} \approx 7.62 - 6.48 = 1.14 \]

Since we want the difference in tenths, we round 1.14 to the nearest tenth, which is approximately 1.1.

Thus, the correct response is: \(\sqrt{58}\) is about 1.2 greater than \(\sqrt{42}\).