What is the largest integer whose square root is an irrational number between 3 and 4?(1 point) @bot
The largest integer whose square root is an irrational number between 3 and 4 is 15.
Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, we add 2 and 2 1/4, and then divide by 2.
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4
Dividing 17/4 by 2:
(17/4) ÷ 2 = (17/4) × (1/2) = 17/8
Converting 17/8 to a mixed number:
17 ÷ 8 = 2 remainder 1
Thus, the rational number between 2 and 2 1/4 using the given method is 2 1/8.
Find a rational number with one decimal place that is between 17−−√ and 18
To find a rational number with one decimal place that is between √17 and 18, we can use the method of averaging.
First, let's find the decimal approximations for √17 and 18:
√17 ≈ 4.123
18
To find the rational number between these two numbers, we can average them:
(4.123 + 18) / 2 ≈ 11.062
Therefore, a rational number with one decimal place between √17 and 18 is approximately 11.1.
incorrect
Apologies for the incorrect response. Let's try again:
To find a rational number with one decimal place between √17 and 18, we can estimate the square root of 17 and 18 to one decimal place:
√17 ≈ 4.1
√18 ≈ 4.2
Let's find the average of 4.1 and 4.2 to obtain the rational number:
(4.1 + 4.2) / 2 = 8.3 / 2 = 4.15
Therefore, a rational number with one decimal place between √17 and 18 is 4.15.
wrong
Apologies for the mistake. Let's try again to find a rational number with one decimal place between √17 and 18.
We can approximate the square root of 17 to one decimal place as √17 ≈ 4.1.
Now, we need to find a rational number between 4.1 and 18. To do this, we can choose a decimal number between 4.1 and 18 and convert it to a rational number.
Let's choose 8 as our decimal number.
Converting 8 to a rational number with one decimal place, we get 8.0.
Therefore, a rational number with one decimal place between √17 and 18 is 8.0.
To find the largest integer whose square root is an irrational number between 3 and 4, we can start by finding the square of 3 and the square of 4, and then check the integers in between to see if their squares fall within the given range.
The square of 3 is 9, and the square of 4 is 16. Since we are looking for an irrational number between these two, we need to find an integer whose square falls between 9 and 16.
Starting with 3, the next integer is 4. When we square 4, we get 16, which is outside the given range. Moving to the next integer, 5, its square is 25, which is also outside the range.
After checking a few more numbers, we find that the square of 6 is 36, which is outside the desired range. However, the square of 7 is 49, which falls within the given range.
So, the largest integer whose square root is an irrational number between 3 and 4 is 7.