What is the largest integer whose square root is an irrational number between 3 and 4?
The largest integer whose square root is an irrational number between 3 and 4 is 15.
To find this, we can start by squaring the lower and upper bounds, 3 and 4, to see which integers they lie between:
3^2 = 9
4^2 = 16
We want to find an integer whose square root is between these two values. Since the square root of 16 is 4, which is greater than 3 and 3 is less than 4, we can conclude that the largest integer whose square root is between 3 and 4 is less than or equal to 15.
Now we can check whether the square root of 15 is an irrational number:
√15 ≈ 3.87298...
Since the square root of 15 is an irrational number and it falls between 3 and 4, we have our answer: the largest integer whose square root is an irrational number between 3 and 4 is 15.
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, we follow these steps:
1. Add 2 and 2 1/4:
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4
2. Divide the sum by 2:
(17/4) ÷ 2 = 17/4 × 1/2 = 17/8
Now, let's write the answer as a mixed number:
17 divided by 8 is equal to 2 with a remainder of 1.
Therefore, the rational number between 2 and 2 1/4 obtained using the method of adding the numbers together and dividing by 2 is 2 1/8.
4.2 is correct
Apologies for the repeated mistakes. Let's re-evaluate the problem.
We know that the square root of 17 lies between 4 and 5, while the square root of 18 lies between 4 and 5 as well.
To find a rational number between these square roots, we need to consider the decimal part of the square roots.
The square root of 17 is approximately 4.123 and the square root of 18 is approximately 4.242.
Considering the decimal part, we can see that:
0.123 < 0.2
Hence, a rational number between the square roots of 17 and 18 with one decimal place would be:
4.2
Therefore, the correct rational number with one decimal place between √17 and √18 is 4.2.
Once again, I apologize for the confusion and the previous incorrect answers.