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

Answer 1

To find where \(\sqrt{38}\) lies on a number line, we can first estimate its value.

We know that:

• \(6^2 = 36\)
• \(7^2 = 49\)

Since \(36 < 38 < 49\), we know that: \[ 6 < \sqrt{38} < 7 \]

Next, we can refine our estimate by squaring numbers between 6 and 7 to find a closer approximation:

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

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

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

So the correct response is: Between 6.1 and 6.2.