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−−√
.

Answer 1

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

1. The square root of 42 can be estimated: \[ \sqrt{42} \approx 6.48 \quad \text{(since \( 6.5^2 = 42.25 \) and \( 6.4^2 = 40.96 \))} \]

2. The square root of 58 can be estimated: \[ \sqrt{58} \approx 7.62 \quad \text{(since \( 7.6^2 = 57.76 \) and \( 7.7^2 = 59.29 \))} \]

Next, let's find the difference: \[ \sqrt{58} - \sqrt{42} \approx 7.62 - 6.48 = 1.14 \]

Rounding this to the nearest tenth gives us approximately 1.1.

Among the response options, the one that correctly states the relationship is: \[ \sqrt{58} \text{ is about 1.2 greater than } \sqrt{42}. \]

Hence, the best choice is: 58−−√ is about 1.2 greater than 42−−√.