What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
6
6
26
26
13
13
25
25
26
Which option shows a rational number between 7.004 and 7.005?(1 point)
Responses
7.0045
7.0045
7451,000
7 Start Fraction 45 over 1,000 End Fraction
7.0054
7.0054
There is no rational number between 7.004 and 7.005.
There is no rational number between 7.004 and 7.005.
7.0045
Which irrational number is between 14−−√ and 18−−√?(1 point)
Responses
13−−√
start root 13 end root
10−−√
start root 10 end root
15−−√
start root 15 end root
19−−√
15−−√ (start root 15 end root)
How many irrational numbers are there between 11−−√ and 17−−√?(1 point)
Responses
twenty-eight numbers
twenty-eight numbers
six numbers
six numbers
four numbers
four numbers
an infinite number
an infinite number
Which option shows a rational number between 3.25678 and 3.25679?(1 point)
Responses
3.25672
3.25672
There are no rational numbers between these two numbers.
There are no rational numbers between these two numbers.
3.256795
3.256795
3.256785
3.256795
To find the least integer whose square root is an irrational number between 5 and 7, we need to check the square roots of integers in that range starting from the smallest integer.
We can start by checking the square root of 6. The square root of 6 is approximately 2.44, which is less than 5.
Next, we can check the square root of 26. The square root of 26 is approximately 5.1, which falls within the range of 5 and 7. However, 26 is not the smallest integer.
Continuing, we check the square root of 13. The square root of 13 is approximately 3.61, which is less than 5.
Finally, we check the square root of 25. The square root of 25 is exactly 5. Since this falls within the range of 5 and 7, it is the smallest integer whose square root is an irrational number between 5 and 7.
Therefore, the correct answer is 25.