Between which pair of rational numbers on a number line does 38−−√

Question

 lie?(1 point)
Responses

Between 6.3 and 6.5
Between 6.3 and 6.5

Between 19 and 19.2
Between 19 and 19.2

Between 18.9 and 19.1
Between 18.9 and 19.1

Between 6.1 and 6.2
Between 6.1 and 6.2
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Answer 1

To determine between which pair of rational numbers \( \sqrt{38} \) lies, we can first calculate \( \sqrt{38} \).

We know that:

• \( 6^2 = 36 \)
• \( 7^2 = 49 \)

So, \( \sqrt{38} \) lies between 6 and 7. To narrow it down further, we can find decimal values:

Calculating \( 6.1^2 \) and \( 6.2^2 \):

• \( 6.1^2 = 37.21 \)
• \( 6.2^2 = 38.44 \)

Since \( 37.21 < 38 < 38.44 \), we conclude that: \[ 6.1 < \sqrt{38} < 6.2 \]

Thus, \( \sqrt{38} \) lies between 6.1 and 6.2.

The correct response is: Between 6.1 and 6.2.