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 1.8 greater than 42−−√
.
square root of 58 is about 1.8 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 1.2 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−−√
.
square root of 58 is about 1.2 greater than square root of 42.

Answer 1

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

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

   • Since \( 6^2 = 36 \) and \( 7^2 = 49 \), we know \( \sqrt{42} \) lies between 6 and 7.
   • A more precise calculation shows \( \sqrt{42} \approx 6.48 \).

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

   • Since \( 7^2 = 49 \) and \( 8^2 = 64 \), we know \( \sqrt{58} \) lies between 7 and 8.
   • A more precise calculation shows \( \sqrt{58} \approx 7.62 \).

Now we can find the approximate difference between these two values:

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

Rounding this to the nearest tenth gives us approximately 1.1.

Thus, the answer is that \( \sqrt{58} \) is about 1.2 greater than \( \sqrt{42} \).

The closest response to this finding from your provided options is:

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