What is the largest integer square root is an irrational number between 3 and 4?
The largest integer whose square root is an irrational number between 3 and 4 is 3.
To find the largest integer whose square root is an irrational number between 3 and 4, we can square integers within this range until we find a number whose square is greater than 4. Let's start with the lower limit of 3.
When we square 3, we get 3^2 = 9, which is greater than 4. Since the square root of 9 is 3, which is not an irrational number, we continue.
When we square 4, we get 4^2 = 16, which is also greater than 4. However, the square root of 16 is 4, which is not an irrational number.
So, the largest integer whose square root is an irrational number between 3 and 4 is 3.
To find the largest integer whose square root is an irrational number between 3 and 4, we need to determine the largest perfect square less than 4. Since 4 is a perfect square, we will exclude it.
Starting with 3, we square each integer until we reach 4:
3^2 = 9
4^2 = 16
The largest perfect square less than 4 is 9. Now, we need to find the largest integer whose square root is an irrational number. Taking the square root of 9, we get 3. Since the square root of 9 is a rational number, we need to go one step back and take the square root of the previous perfect square.
Therefore, the largest integer whose square root is an irrational number between 3 and 4 is the square root of 4, which is 2.