What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
25
25
6
6
26
26
13
The least integer whose square root is an irrational number between 5 and 7 is 26.
Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
165
Start Fraction 16 over 5 end fraction
103
Start Fraction 10 over 3 end fraction
3.4
3.4
3.1
To find the least integer whose square root is an irrational number between 5 and 7, we need to look for a perfect square between 5^2 (25) and 7^2 (49).
Starting with the smallest value, which is 25, we can take the square root of 25. The square root of 25 is 5, which is not between 5 and 7.
Moving on to the next integer, which is 6, let's calculate the square root of 6. The square root of 6 is approximately 2.449, which is also not between 5 and 7.
Continuing to the next integer, which is 26, the square root of 26 is approximately 5.099, which is between 5 and 7.
Therefore, 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 can simply check the squares of integers within that range.
Starting with the lower limit of 5, we take the square of each integer until we find one whose square root falls within the desired range.
For example, 5 squared is 25, and its square root is 5. Since the square root of 25 is not between 5 and 7, we move to the next integer.
Next, we check 6 squared, which is 36. The square root of 36 is 6. Since 6 is between 5 and 7, we have found an integer whose square root is an irrational number between 5 and 7.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 6.