Question

Compare 42−−√ and 58−−√ plotted on the number line. What is the approximate difference in tenths between the two values?(1 point)Responses58−−√ is about 1.2 greater than 42−−√.square root of 58 is about 1.2 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 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.

Answer 1

To compare \(\sqrt{42}\) and \(\sqrt{58}\), we can calculate their approximate values:

• The square root of 42 is approximately: \[ \sqrt{42} \approx 6.48 \]

• The square root of 58 is approximately: \[ \sqrt{58} \approx 7.62 \]

Now, we can find the difference between these two values: \[ \sqrt{58} - \sqrt{42} \approx 7.62 - 6.48 = 1.14 \]

This difference can be rounded to one decimal place, giving us approximately 1.1.

Among the given options, the closest statement to our calculation is: 58−−√ is about 1.2 greater than 42−−√. square root of 58 is about 1.2 greater than square root of 42.