Which number line best shows the position of square root of 13?

Question

Group of answer choices

Number line with numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4 labeled. A dot is made at 1.3 and labeled as square root of 13.

Number line with numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4 labeled. A dot is made at 2.6 and labeled as square root of 13.

Number line with numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4 labeled. A dot is made at 3.6 and labeled as square root of 13.

Number line with numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4 labeled. A dot is made at 4.3 and labeled as square root of 13.

Answer 1

To find the correct position of \(\sqrt{13}\) on a number line, we first need to calculate \(\sqrt{13}\).

Calculating the approximate value, we find:

• \(\sqrt{9} = 3\) (since \(3^2 = 9\))
• \(\sqrt{16} = 4\) (since \(4^2 = 16\))

Since \(13\) is between \(9\) and \(16\), it follows that: \[ 3 < \sqrt{13} < 4. \]

To get a more precise value, we know: \[ \sqrt{13} \approx 3.60555. \]

Now we round this to one decimal place, which gives us: \[ \sqrt{13} \approx 3.6. \]

This means \(\sqrt{13}\) is closest to 3.6 on the number line.

Given the answer choices, the correct number line is the one that has a dot made at 3.6 labeled as \(\sqrt{13}\).

Thus, the correct choice is the number line with a dot made at 3.6 and labeled as square root of 13.