What is the least integer whose square root is an irrational number between 5 and 7
No, the least integer whose square root is an irrational number between 5 and 7 is 26
To find the least integer whose square root is an irrational number between 5 and 7, we need to find the smallest perfect square greater than 5^2 (25) and the largest perfect square less than 7^2 (49).
The smallest perfect square greater than 25 is 6^2 (36), and the largest perfect square less than 49 is 7^2 (49).
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 37.
To find the least integer whose square root is an irrational number between 5 and 7, we need to identify the integers whose square roots fall within this range.
First, let's find the smallest perfect square greater than 5. The square of 3 is 9, and the square of 4 is 16. So, the square root of 9 is 3, and the square root of 16 is 4. This means that the square root of any integer greater than 16 will be greater than 4.
Next, let's find the largest perfect square smaller than 7. The square of 2 is 4, and the square of 3 is 9. This means that the square root of any integer smaller than or equal to 4 will be less than or equal to 2.
Therefore, we are looking for an integer larger than 16 and smaller than or equal to 4. However, such an integer does not exist since no number can be both larger than 16 and smaller than or equal to 4.
Hence, there is no integer whose square root is an irrational number between 5 and 7.
To find the least integer whose square root is an irrational number between 5 and 7, we need to find the smallest integer whose square is between the squares of 5 and 7.
The square of 5 is 25, and the square of 7 is 49. Any integer between 5 and 7 (excluding 5 and 7) will have a square between 25 and 49.
The smallest integer whose square is between 25 and 49 is 6. The square of 6 is 36.
Thus, the least integer whose square root is an irrational number between 5 and 7 is 6.
Apologies for the incorrect answer. You are correct.
To find the least integer whose square root is an irrational number between 5 and 7, we can start by finding the square root of 5 and 7.
The square root of 5 is approximately 2.236, and the square root of 7 is approximately 2.646.
The least integer whose square root is an irrational number between 5 and 7 is the smallest integer greater than 2.646, which is 3. The square of 3 is 9, which is greater than 7.
So, the least integer whose square root is an irrational number between 5 and 7 is 3.