Which of the following is an irrational number between 5 and 7:
√6, √12, √27, √36?
13 answers
The irrational number between 5 and 7 is √6.
Wrong
I apologize for the mistake. The correct irrational number between 5 and 7 is √6.
It was √27
You are correct. I apologize for the mistake. The correct irrational number between 5 and 7 is √27. Thank you for correcting me.
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.
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 first add the numbers:
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4
Next, we divide the sum by 2:
17/4 ÷ 2 = 17/4 × 1/2 = 17/8
So, a rational number between 2 and 2 1/4 using this method is 17/8, which can be written as a mixed number as 2 1/8.
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4
Next, we divide the sum by 2:
17/4 ÷ 2 = 17/4 × 1/2 = 17/8
So, a rational number between 2 and 2 1/4 using this method is 17/8, which can be written as a mixed number as 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 take the average of √17 and √18.
√17 is approximately 4.123
√18 is approximately 4.242
Now, we find the average of these two numbers:
(4.123 + 4.242) / 2 = 8.365 / 2 = 4.1825
So, a rational number with one decimal place that is between √17 and √18 is approximately 4.2.
√17 is approximately 4.123
√18 is approximately 4.242
Now, we find the average of these two numbers:
(4.123 + 4.242) / 2 = 8.365 / 2 = 4.1825
So, a rational number with one decimal place that is between √17 and √18 is approximately 4.2.
Which of the following is between pi and √11?
A. √7
B. √12
C. √10
D. √8
A. √7
B. √12
C. √10
D. √8
To determine which of the numbers is between pi and √11, we can compare the values of each option to the given numbers.
Approximating the values:
pi is approximately 3.14159
√11 is approximately 3.31662
Now we can compare the approximations:
A. √7 ≈ 2.64575 (smaller than both pi and √11)
B. √12 ≈ 3.46410 (greater than √11)
C. √10 ≈ 3.16228 (greater than pi and smaller than √11)
D. √8 ≈ 2.82843 (greater than both pi and √11)
From the options given, the only number that falls between pi and √11 is √10 (option C). Therefore, the correct answer is C.
Approximating the values:
pi is approximately 3.14159
√11 is approximately 3.31662
Now we can compare the approximations:
A. √7 ≈ 2.64575 (smaller than both pi and √11)
B. √12 ≈ 3.46410 (greater than √11)
C. √10 ≈ 3.16228 (greater than pi and smaller than √11)
D. √8 ≈ 2.82843 (greater than both pi and √11)
From the options given, the only number that falls between pi and √11 is √10 (option C). Therefore, the correct answer is C.