Question

What is the least integer who square root is an irrational number between five and seven with the answer be six 1326 or 25

Answer 1

To find the least integer whose square root is an irrational number between five and seven, we need to first determine the range of numbers whose square roots fall within that interval.

The square of 5 is \(5^2 = 25\) and the square of 7 is \(7^2 = 49\). Therefore, we are looking for integers between 25 and 49.

The integers in this range are: 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48.

Now we want to identify the smallest of these that produces an irrational square root. The square roots of perfect squares within this interval (which yield rational results) are:

- \(36\) (the square root is \(6\))
- \(49\) (the square root is \(7\))

All other squares (those not perfect squares) will have irrational square roots. The smallest integer greater than 25 that is not a perfect square is \(26\).

Thus, the least integer whose square root is an irrational number between 5 and 7 is:

\[
\boxed{26}
\]