Using rational approximations, what is an inequality statement comparing π
and 8–√
?
To find a rational approximation of π, we can use the fraction 22/7. Similarly, we can use the square root of 8 as an approximation of √8.
So, we have π ≈ 22/7 and 8–√8 ≈ 8–2.828 ≈ 5.172.
Comparing the two approximations, we can say that π is greater than 8–√8.
Thus, the inequality statement comparing π and 8–√8 is π > 8–√8.
To compare π and 8–√, we can use rational approximations for the values.
Rational approximation of π: π ≈ 3.14
Rational approximation of 8–√: 8–√ ≈ 6.59
Now, we can write the inequality statement comparing the two:
π < 8–√
Therefore, the inequality statement is π < 8–√.
To compare the values of π and 8 - √2 using rational approximations, we can find the decimal approximations for both and compare them.
First, let's find an approximation for π. The commonly used approximation is 3.14.
Next, let's find an approximation for 8 - √2. We know that √2 is approximately 1.41. Subtracting this from 8 gives us 8 - 1.41 ≈ 6.59.
Now we can compare the two decimal approximations:
π ≈ 3.14
8 - √2 ≈ 6.59
To write an inequality statement comparing π and 8 - √2, we can say:
π < 8 - √2
Note that this comparison is based on the given rational approximations, so it may not be completely accurate.