Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
The inequality is: 81−−√ > 8–√8.
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To compare the two expressions, we can use rational approximations to estimate their values.
First, let's find the rational approximation for √81:
√81 is equal to 9, since 9 squared equals 81.
Next, let's find the rational approximation for √8:
√8 is approximately 2.83, rounded to two decimal places.
Now, we can compare the two expressions:
81−−√ = 9
8–√8 ≈ 2.83
Since 9 is greater than 2.83, we can write the inequality as:
81−−√ > 8–√8
To find the inequality statement comparing the two numbers, we can use rational approximations to get a decimal representation of the square roots.
First, let's find the rational approximation for √81:
√81 ≈ 9
Next, let's find the rational approximation for √8:
√8 ≈ 2.828
Now we can compare the two:
9 > 2.828
Therefore, the inequality statement comparing 81−−√ and 8–√8 is:
81−−√ > 8–√8