What is the least integer whose square root is an irrational number between 5 and 7?
25
6
26
13
The least integer whose square root is an irrational number between 5 and 7 is 26.
show your work
To find the least integer whose square root is an irrational number between 5 and 7, we need to find the smallest perfect square that is greater than 25 (the square of 5) and less than 49 (the square of 7).
The smallest perfect square greater than 25 is 36, and its square root is √36 = 6. This is not within the desired range of numbers.
The next perfect square is 49, and its square root is √49 = 7. Since 7 is included in the desired range, we know that there is an integer whose square root is within this range.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 26.
you're positive its 26
Apologies for the incorrect response. Let's re-evaluate the problem.
We need to find the least integer whose square root is an irrational number between 5 and 7. The square of 5 is 25, and the square of 7 is 49.
Let's check the possible integers between 25 and 49 to find the desired square root.
The square root of 26 is approximately 5.099 and is an irrational number between 5 and 7.
Therefore, 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---
3.4
3.1
16/5
10/3
To find an example of a rational number between √10 and √11, we can approximate the square roots to a decimal and choose a rational number between them.
√10 ≈ 3.162
√11 ≈ 3.317
One rational number that lies between these approximations is 3.4.
Therefore, 3.4 is an example of a rational number between √10 and √11.
you are positive?
Apologies for the incorrect response. Let's re-evaluate the problem.
To find a rational number between √10 and √11, we can approximate the square roots to a decimal and choose a rational number between them:
√10 ≈ 3.162
√11 ≈ 3.317
One rational number that lies between these approximations is 3.2.
Therefore, 3.2 is an example of a rational number between √10 and √11.