What is the largest integer whose square root is an irrational number between 3 and 4?(1 point)
The largest integer whose square root is an irrational number between 3 and 4 is 15.
why
To determine the largest integer whose square root is an irrational number between 3 and 4, we need to find the largest perfect square that is less than 16 (since 16 is the square of the largest integer less than 4). The largest perfect square less than 16 is 9, which is the square of 3. Therefore, the largest integer whose square root is an irrational number between 3 and 4 is 15.
Find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we will add 2 and 214 and divide the sum by 2.
2 + 214 = 216
216 ÷ 2 = 108
108 is a rational number between 2 and 214. As a mixed number, it is written as 108/1 or simply 108.
a different number?
If the goal is to find a different rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we can choose any two numbers between 2 and 214 and follow the same steps.
Let's choose the numbers 20 and 200:
20 + 200 = 220
220 ÷ 2 = 110
110 is a rational number between 2 and 214. As a mixed number, it is written as 110/1 or simply 110.
Find a rational number with one decimal place that is between 17−−√ and 18−−√.
To find a rational number with one decimal place between √17 and √18, we can take the average of the two square roots:
(√17 + √18) / 2 ≈ 4.162
Therefore, a rational number with one decimal place that is between √17 and √18 is approximately 4.162.
Which of the following is between π and 11−−√?(1 point)
Responses
7–√
Start Root 7 End Root
8–√
Start Root 8 End Root
12−−√
Start Root 12 End Root
10−−√
Start Root 10 End Root