Show an example of a rational number that is between 10−−√ and 11−−√.(1 point
An example of a rational number between √10 and √11 is 3.16.
Which irrational number is between 14−−√ and 18−−√?(1 point)
To find a rational number between √10 and √11, we can take the average of these two numbers. Let's calculate it step by step:
Step 1: Calculate the average:
(√10 + √11) / 2
Step 2: Simplify the expression:
(√10 + √11) / 2 ≈ (3.16 + 3.32) / 2
Step 3: Evaluate the expression:
(3.16 + 3.32) / 2 ≈ 6.48 / 2 ≈ 3.24
Therefore, the rational number between √10 and √11 is approximately 3.24.
To find a rational number between √10 and √11, we can take the average (also known as the midpoint) of these two numbers.
The average can be calculated as follows:
Average = (√10 + √11) / 2
Now, let's compute this average to find the rational number between √10 and √11:
Average = (√10 + √11) / 2
≈ (3.162 + 3.317) / 2
≈ 6.479 / 2
≈ 3.2395
Therefore, the rational number between √10 and √11 is approximately 3.2395.
√16 is equal to 4 and √18 is approximately equal to 4.24.
Therefore, an example of an irrational number between √14 and √18 is √16 = 4.