Using rational approximations, what is an inequality statement comparing π and 8–√? Enter <, >, or =.(1 point)
The inequality is: π
8–√.
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its not the right answer
I apologize for the mistake. The correct inequality statement comparing π and 8–√ is:
π > 8–√
ty
You're welcome! If you have any more questions, feel free to ask.
To compare π and 8 – √, we can use rational approximations.
One rational approximation for π is 3.14.
To find a rational approximation for 8 – √, we can simplify it as follows:
8 – √ = 8 – √1 = 8 – 1 = 7.
So, the inequality statement comparing π and 8 – √ is:
π < 8 – √.
To compare π and 8–√ using rational approximations, we need to find the decimal approximations for both and then compare them.
First, let's find the decimal approximation for π. π is an irrational number and cannot be expressed as an exact decimal. However, we can use a rational approximation, such as 3.14 or 22/7.
Next, let's find the decimal approximation for 8–√. To do this, we'll subtract the square root of a rational number from 8. Let's approximate the square root of 2 as 1.41. Therefore, 8–√ ≈ 8 - 1.41 = 6.59.
Now we can compare the decimal approximations:
π ≈ 3.14
8–√ ≈ 6.59
From these approximations, we can see that π is less than 8–√, so the inequality statement is:
π < 8–√