Find a rational number with one decimal place that is between 17−−√ and 18−−√.(1 point)
Apologies for the incorrect response.
Let's try another approach. We can rewrite the square roots in decimal form approximations and then find a rational number between them.
√17 ≈ 4.123
√18 ≈ 4.243
Since we're looking for a rational number with one decimal place, we can take the average of these two approximations.
Average = (4.123 + 4.243) / 2 ≈ 4.183
Therefore, a rational number with one decimal place that is between √17 and √18 is approximately 4.2.
To find a rational number between √17 and √18, we can take the average of the two numbers.
Average = (√17 + √18) / 2
Using a calculator, we find that (√17 + √18) is approximately 8.9435.
Dividing this by 2, we get 4.4718.
Therefore, a rational number with one decimal place that is between √17 and √18 is approximately 4.5.
thats not right
To find a rational number between √17 and √18, we need to find two consecutive perfect squares that the square roots lie between.
The perfect squares closest to 17 are 16 and 25. Taking the square root of both of these perfect squares, we get √16 = 4 and √25 = 5.
Since √17 is between 4 and 5, and √18 is between 4 and 5 as well, a rational number between them can be found by taking the average of the two square roots:
(4 + 5) / 2 = 9 / 2 = 4.5
Therefore, a rational number with one decimal place that is between √17 and √18 is 4.5.
To find a rational number with one decimal place between √17 and √18, we can follow these steps:
Step 1: Express √17 and √18 as decimal numbers.
Using a calculator, we find that √17 ≈ 4.123 and √18 ≈ 4.243.
Step 2: Identify the whole number part of each decimal.
The whole number part of 4.123 is 4, and the whole number part of 4.243 is also 4.
Step 3: Determine the possible rational number options.
Since the whole number part is the same, we need to focus on the decimal part to find a rational number between √17 and √18.
The possible rational numbers with one decimal place include 4.1, 4.2, and 4.3.
Step 4: Determine if any of the possible rational numbers are between √17 and √18.
By comparing the decimal parts to the decimal approximations of √17 and √18, we can see that 4.2 is the only rational number between √17 and √18.
Therefore, the rational number with one decimal place that is between √17 and √18 is 4.2.