Asked by Preston
Show an example of a rational number that is between √10 √11
3.4
16/5
3.1
10/3
3.4
16/5
3.1
10/3
Answers
Answered by
GPT 3.5
One example of a rational number between √10 and √11 is 16/5.
To verify that 16/5 lies between √10 and √11, we can convert them to decimal approximations:
√10 is approximately equal to 3.16228
√11 is approximately equal to 3.31662
The decimal approximation of 16/5 is 3.2, which falls between 3.16228 and 3.31662.
Therefore, 16/5 is a rational number that lies between √10 and √11.
To verify that 16/5 lies between √10 and √11, we can convert them to decimal approximations:
√10 is approximately equal to 3.16228
√11 is approximately equal to 3.31662
The decimal approximation of 16/5 is 3.2, which falls between 3.16228 and 3.31662.
Therefore, 16/5 is a rational number that lies between √10 and √11.
Answered by
GPT 3.5
3.1
Answered by
GPT 3.5
One irrational number that is between √14 and √18 is √15.
To verify that √15 lies between √14 and √18, we can convert them to decimal approximations:
√14 is approximately equal to 3.74
√18 is approximately equal to 4.24
The decimal approximation of √15 is approximately equal to 3.87.
Since 3.74 < 3.87 < 4.24, √15 is indeed an irrational number that lies between √14 and √18.
To verify that √15 lies between √14 and √18, we can convert them to decimal approximations:
√14 is approximately equal to 3.74
√18 is approximately equal to 4.24
The decimal approximation of √15 is approximately equal to 3.87.
Since 3.74 < 3.87 < 4.24, √15 is indeed an irrational number that lies between √14 and √18.
Answered by
GPT 3.5
The answer is √15.
Answered by
GPT 3.5
There are an infinite number of irrational numbers between √11 and √17.