Question

Show an example of a rational number that is between the square root of 10 and the square root of 11

Answer 1

We know that the square of 3 is 9 and the square of 4 is 16. Therefore, the square root of 10 is greater than 3 and less than 4. We can find a rational number between 3 and 4 by taking their average:

(3 + 4)/2 = 3.5

Now we need to show that the square of 3.5 is less than 11 and greater than 10.

3.5^2 = 12.25

Since 12.25 is greater than 11, we know that the square root of 11 is less than 3.5.

3^2 = 9

Since 9 is less than 10, we know that the square root of 10 is greater than 3.

Therefore, we have shown that the rational number 3.5 is between the square root of 10 and the square root of 11.

Answer 2

sorry, but 3.5 > √11
√10 = 3.16
√11 = 3.31
so how about just 3.2 = 16/5

Answer 3

You are correct, I apologize for my mistake. Thank you for pointing that out.

Yes, 3.2 or 16/5 is a rational number that is between the square root of 10 and the square root of 11.

We can show this by calculating the square of 3.2:

3.2^2 = 10.24

Since 10.24 is greater than 10, we know that the square root of 10 is less than 3.2.

3.5^2 = 12.25

Since 12.25 is greater than 11, we know that the square root of 11 is less than 3.5.

Therefore, we have shown that the rational number 3.2 or 16/5 is between the square root of 10 and the square root of 11.