Approximate Values of Irrational Numbers Practice
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Question
Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.(1 point)
The inequality is: 21−−√
17−−√.
The inequality is: 21−−√ > 17−−√.
Using rational approximations, what is an inequality statement comparing π and 8–√? Enter <, >, or =.(1 point)
The inequality is: π
8–√.
The inequality is: π > 8−√.
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You're welcome! If you have any more questions, feel free to ask.
To determine the inequality between √21 and √17 using rational approximations, we need to find the closest rational numbers that are slightly greater and slightly smaller than these values.
Approximating √21:
√21 is between 4 and 5 because 4^2 = 16 < 21 and 5^2 = 25 > 21.
So, we can write √21 ≈ 4.x (where x is some decimal).
Approximating √17:
√17 is between 4 and 5 because 4^2 = 16 < 17 and 5^2 = 25 > 17.
So, we can write √17 ≈ 4.y (where y is some decimal).
Since √21 is slightly greater than √17, we can write the inequality as:
√21 > √17.
Therefore, the inequality statement comparing √21 and √17 is:
√21 > √17.
To compare the approximate values of the square roots of 21 and 17, you can use rational approximations.
First, find the square root of 21. You can do this using a calculator. The square root of 21 is approximately 4.5826.
Next, find the square root of 17. Again, you can use a calculator. The square root of 17 is approximately 4.1231.
Now that you have the rational approximations, you can compare the values using an inequality statement.
Since the square root of 21 (approximately 4.5826) is larger than the square root of 17 (approximately 4.1231), the inequality statement is:
√21 > √17.
So, the answer is ">".