What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
6
6
13
13
25
25
26
The least integer whose square root is 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
3.1
3.1
3.4
An example of a rational number that is between √10 and √11 is 16/5.
To find the least integer whose square root is an irrational number between 5 and 7, we can start by finding the square of each number within the given range.
The squares of the numbers 5 and 7 are:
- 5^2 = 25
- 7^2 = 49
Next, we can determine the squares of the integers between 5 and 7 to see if any of them have an irrational square root.
The squares of the integers 6 and 7 are:
- 6^2 = 36
- 7^2 = 49
Since the square root of 36 is 6, which is not an irrational number, and the square root of 49 is 7, which is not between 5 and 7, we need to check the next integer.
The square of the integer 8 is:
- 8^2 = 64
The square root of 64 is 8, which is not between 5 and 7.
Continue this process for the next integer, which is 9:
- 9^2 = 81
The square root of 81 is 9, which is also not between 5 and 7.
Finally, we check the square of the integer 10:
- 10^2 = 100
The square root of 100 is 10, which does not meet the criteria.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 13.