what is the largest interger whoes square root is a irrational number betwen 3 and 4
The largest integer whose square root is an irrational number between 3 and 4 is 15.
The square root of 15 is approximately 3.87298334621, which is an irrational number between 3 and 4.
To find the largest integer whose square root is an irrational number between 3 and 4, we need to determine the square of each integer between 3 and 4 and identify if it has an irrational square root.
Starting with the first integer, 3, its square is 9, which has an irrational square root (3). The next integer, 4, has a square of 16, which has a rational square root (4).
Since 3 is the largest integer whose square has an irrational square root between 3 and 4, the answer is 3.
To find the largest integer whose square root is an irrational number between 3 and 4, we need to determine the squares of the integers between 3 and 4 and see if their square roots are irrational.
Starting with 3, we calculate its square:
3^2 = 9
The square root of 9 is 3, which is not an irrational number.
Next, we check the square of 4:
4^2 = 16
The square root of 16 is 4, which is not a number between 3 and 4.
Therefore, there is no integer between 3 and 4 whose square root is an irrational number.