Question

Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =

Answer 1

[AI-generated answer — Bot GPT 3.5]

To compare the values of 81−−√ and 8–√8, we can rewrite both numbers as rational approximations.

81−−√ can be approximated as 9, while 8–√8 can be approximated as 2.8284.

Therefore, we have 9 > 2.8284.

Thus, the inequality statement comparing 81−−√ and 8–√8 is 81−−√ > 8–√8.

Answer 2

Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.

Answer 3

bot?

Answer 4

[AI-generated answer — Step-by-Step Bot]

To compare 81−−√ and 8–√8 using rational approximations, we can simplify both expressions.

Starting with 81−−√, we know that √81 equals 9. So, 81−−√ can be simplified to just 9.

Now, let's simplify 8–√8. The square root of 8 is approximately 2.8284, rounded to four decimal places. Therefore, 8–√8 can be approximated as 8 - 2.8284, which is approximately 5.1716.

Comparing the simplified forms, we have 9 > 5.1716.

Therefore, the inequality statement comparing 81−−√ and 8–√8 is 9 > 5.1716.

Answer 5

[AI-generated answer — Explain Bot]

To compare the values of √81 and √8, we can approximate the square roots using rational numbers.

Let's start with √81. Since 9^2 = 81, we know that √81 = 9.

Now let's consider √8. To approximate this square root, we need to find the closest perfect squares to 8. We know that 2^2 = 4 and 3^2 = 9. Since 8 is between 4 and 9, we can estimate that √8 is slightly greater than 2 but less than 3.

Therefore, we have √81 = 9 and √8 ≈ 2.x (where x is a decimal between 2 and 3).

Since 9 is greater than any number between 2 and 3, we can conclude that 81−−√ > 8–√8. So the correct inequality statement is:

√81 > √8

Therefore, the answer is > (greater than).