What is the least integer whose square root is an irrational number between 5 and 7?

Question

A. 13

B. 6

C. 25

D. 26

Answer 1

To solve this problem, we need to find the least possible integer $n$ such that $\sqrt{n}$ is between 5 and 7. To find the least possible $n$, we can start by finding the square of 5 and the square of 6, and then keep incrementing until we find a square greater than 49 (since 7 squared equals 49).

Squaring 5, we get $5^2 = 25$.

Squaring 6, we get $6^2 = 36$.

Let's calculate the square of 7 to see if it is less than or greater than 49.

Squaring 7, we get $7^2 = 49$.

Since 49 is the smallest square greater than 49, the least possible integer $n$ whose square root is an irrational number between 5 and 7 is $\boxed{\textbf{(D) } 26}$.