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Show an example of an irrational number between 9 and 11. (1 point)
99−−√
start root 99 end root
10−−√
start root 10 end root
20−−√
start root 20 end root
100−−−√
An example of an irrational number between 9 and 11 is (√10) which is approximately 3.162.
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
Responses
25
6
26
13
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 falls within this range.
The square of 5 is 25, and the square root of 5 is approximately 2.236, which is irrational. However, this is not the smallest perfect square within the given range.
The square of 6 is 36, and the square root of 6 is approximately 2.449, which is also irrational. Again, this is not the smallest perfect square within the given range.
The square of 7 is 49, and the square root of 7 is approximately 2.646, which is irrational. This is the smallest perfect square within the given range.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 49.
49 is wrong
I apologize for the mistake. Let's try again.
To find the least integer whose square root is an irrational number between 5 and 7, we need to find the smallest perfect square within this range.
The square of 5 is 25, and the square root of 25 is exactly 5 which is not an irrational number.
The square of 6 is 36, and the square root of 36 is exactly 6 which is also not an irrational number.
The square of 7 is 49, and the square root of 49 is exactly 7 which is not an irrational number.
Based on this, there is no perfect square within the range of 5 and 7 whose square root is an irrational number.
What is the least integer whose square root is an irrational number between 5 and 7?(1 point)
25
6
26
13
To find the least integer whose square root is an irrational number between 5 and 7, we need to check the perfect squares within that range.
The square of 5 is 25, and the square root of 25 is exactly 5. This is not an irrational number.
The square of 6 is 36, and the square root of 36 is exactly 6. This is also not an irrational number.
The square of 7 is 49, and the square root of 49 is exactly 7. Again, this is not an irrational number.
Therefore, there is no least integer between 5 and 7 whose square root is an irrational number.