Question

To two decimal places, square root of, 13, end square root must lie between______ and_____

Answer 1

To find the range between which the square root of 13 lies, we can calculate the squares of some integers around the number 13.

- The square of 3 is \(3^2 = 9\).
- The square of 4 is \(4^2 = 16\).

Since \(9 < 13 < 16\), we find that:

\[
3 < \sqrt{13} < 4
\]

To narrow it down further, we can calculate the square roots of numbers that are closer to 13.

Calculating the square of 3.6:

\[
3.6^2 = 12.96
\]
(so, \(3.6 < \sqrt{13}\))

Now, calculating the square of 3.7:

\[
3.7^2 = 13.69
\]
(so, \(\sqrt{13} < 3.7\))

Now we can confirm that:

\[
3.6 < \sqrt{13} < 3.7
\]

To two decimal places:

\(\sqrt{13} \approx 3.61\)

Therefore, the square root of 13 must lie between **3.60 and 3.61** (approximately).