Find a rational number with one decimal place that is between 17−−√ and 18−−√.
To find a rational number between $\sqrt{17}$ and $\sqrt{18}$, we can average the two numbers. $\sqrt{17}$ is between $\sqrt{16} = 4$ and $\sqrt{25}=5$, so $\sqrt{17}$ is between 4 and 5. $\sqrt{18}$ is between $\sqrt{16} = 4$ and $\sqrt{25}=5$, so $\sqrt{18}$ is between 4 and 5 as well. Therefore, a rational number between $\sqrt{17}$ and $\sqrt{18}$ is $\dfrac{\sqrt{17}+\sqrt{18}}{2}$. When we round this number to one decimal place, we have $\frac{3.9+4.2}{2} = \frac{8.1}{2} = \boxed{4.1}$.
what does \boxed{4.1}$. mean
To find a rational number with one decimal place between 17−−√ and 18−−√, we can estimate their decimal values.
First, let's calculate the decimal value of 17−−√ using a calculator:
17−−√ = 4.123105625617661...
Then, let's calculate the decimal value of 18−−√:
18−−√ = 4.242640687119285...
From these calculations, we can see that the decimal value of the square root of 17 is approximately 4.12, and the decimal value of the square root of 18 is approximately 4.24.
To find a rational number between these values with one decimal place, we can round the decimal values to the nearest tenth.
Rounded values:
Decimal value of 17−−√ ≈ 4.1
Decimal value of 18−−√ ≈ 4.2
Thus, a rational number with one decimal place between 17−−√ and 18−−√ is 4.1.
To find a rational number with one decimal place between √17 and √18, we can start by calculating the values of √17 and √18.
Using a calculator, we find that √17 ≈ 4.1231 and √18 ≈ 4.2426.
A rational number with one decimal place will have the form x = a.b, where a is an integer and b is a single-digit number (0-9).
Now, we need to find an integer a and a single-digit number b such that:
4.1 ≤ a.b ≤ 4.2
To determine the value of a, we can see that the integer part of √17 is 4, and the integer part of √18 is also 4. Since we want a number between these two square roots, we can choose a = 4.
Now, let's check the possible values for b:
4.10 ≤ 4.b ≤ 4.20
Checking the values for b, we find that 4.10 is not between √17 and √18, but 4.20 is. Therefore, we take b = 2.
Hence, the rational number with one decimal place that is between √17 and √18 is 4.2.