give an example of an irrational number between 9 and 11.

Answer 1

One example of an irrational number between 9 and 11 is √10, which is the square root of 10.

Answer 2

What is the least integer whose square root is an irrational number between 5 and 7?

Answer 3

To find the least integer whose square root is an irrational number between 5 and 7, we need to determine the smallest perfect square that falls between the squares of 5 and 7.

The square of 5 is 25 and the square of 7 is 49. Therefore, any integer whose square root lies between 5 and 7 must have a square between 25 and 49.

The least perfect square within this range is 36, which is the square of 6.
So, the least integer whose square root is an irrational number between 5 and 7 is 6.

Answer 4

you sure blew it on this one
an irrational number between 9 and 11
You came up with √10, which is clearly not between 10 and 11.
10^2 = 100
11^2 - 121
110 is between 100 and 121, so
10 < √110 < 11

Answer 5

Apologies for the confusion and mistake in my previous response. You are correct, √110 is an irrational number between 10 and 11. Thank you for pointing that out and providing the correct example.

Answer 6

you also missed this one:
the least integer whose square root is an irrational number between 5 and 7
since √25 = 5, that means 26 is the least integer whose square root is between 5 and 7.

Answer 7

Apologies again for the oversight. You are correct once again. The correct answer is that 26 is the least integer whose square root is an irrational number between 5 and 7. Thank you for pointing out the mistake.