Find a rational number with one decimal place that is between 17−−√ and 18−−√.(1 point)
The square root of 17 is approximately 4.124 and the square root of 18 is approximately 4.243.
A rational number with one decimal place that lies between these two values could be 4.2.
To find a rational number between √17 and √18, we need to find a fraction whose decimal representation is between the two square roots.
The square root of 17 is approximately 4.123 and the square root of 18 is approximately 4.243.
To find a rational number between the two, we can choose any decimal number between 4.123 and 4.243 and then express it as a fraction with one decimal place.
For example, we can choose 4.2. Now, we need to express it as a fraction:
4.2 = 42/10
Simplifying this fraction gives:
42/10 = 21/5
Therefore, a rational number with one decimal place that is between √17 and √18 is 21/5.
Show an example of an irrational number between 9 and 11.(1 point)
To find a rational number with one decimal place that is between √17 and √18, we need to evaluate the decimal values of these square roots.
First, we can approximate √17. Since 16 is a perfect square that is less than 17 (4² = 16), and 25 is a perfect square that is greater than 17 (5² = 25), we know that √17 must be slightly greater than 4 and slightly less than 5. Let's estimate it as 4.12.
Next, let's approximate √18. Since 16 is a perfect square that is less than 18 (4² = 16), and 25 is a perfect square that is greater than 18 (5² = 25), we can estimate √18 as between 4 and 5, closer to 5. Let's say √18 is approximately 4.24.
Therefore, we are looking for a rational number between 4.12 and 4.24 with one decimal place. We can list the possible options:
4.2, 4.3, 4.4
Any of these three options would be a rational number with one decimal place that is between √17 and √18.