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 need to approximate the values of √17 and √18 and then find a rational number in between.
Approximating √17:
Using a calculator, we find that √17 ≈ 4.123105625617661.
Approximating √18:
Using a calculator, we find that √18 ≈ 4.242640687119285.
Since we want a rational number with one decimal place between √17 and √18, we will round the values to one decimal place.
Approximated √17: 4.1
Approximated √18: 4.2
Now, we need to find a rational number between 4.1 and 4.2. One way to do this is to take the average of these two values:
Average of 4.1 and 4.2 = (4.1 + 4.2)/2 = 8.3/2 = 4.15
Therefore, a rational number with one decimal place between √17 and √18 is 4.15.
To find a rational number between √17 and √18, we can use the fact that the decimal representation of a rational number terminates or repeats.
First, let's find the decimal approximation of √17 and √18 using a calculator:
√17 ≈ 4.123105625617661
√18 ≈ 4.242640687119285
Now, let's examine the decimal parts of these square roots:
Decimal part of √17 = 0.123105625617661
Decimal part of √18 = 0.242640687119285
To find a rational number between these two square roots, we can take the average of their decimal parts.
Average = (0.123105625617661 + 0.242640687119285) / 2 = 0.182873156
Therefore, the rational number with one decimal place that is between √17 and √18 is approximately 4.2.