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

58−−√
is about 0.8 greater than 42−−√
.

Answer 1

To compare \( \sqrt{42} \) and \( \sqrt{58} \), we can first estimate their values.

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

   • \( 6^2 = 36 \)
   • \( 7^2 = 49 \)
   • Since \( 42 \) is between \( 36 \) and \( 49 \), \( \sqrt{42} \) is between \( 6 \) and \( 7 \).
   • More accurately, \( \sqrt{42} \approx 6.48 \).

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

   • \( 7^2 = 49 \)
   • \( 8^2 = 64 \)
   • Since \( 58 \) is between \( 49 \) and \( 64 \), \( \sqrt{58} \) is between \( 7 \) and \( 8 \).
   • More accurately, \( \sqrt{58} \approx 7.62 \).

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

To express this difference in tenths, we can say: \[ 1.14 \approx 1.2 \]

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

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