Using rational approximations, what is an inequality statement comparing 81−−√

Question

and 8–√8
? Enter <, >, or =.

explain how < is the correct answer

Answer 1

To compare the two expressions 81−−√ and 8–√8 using rational approximations, we can find the square root of both numbers and compare them.

First, let's find the square root of 81. The closest square root that is a rational number is 9, since 9 squared is 81.

Next, let's find the square root of 8. The closest square root that is a rational number is 2, since 2 squared is 4, which is less than 8.

Therefore, we have 81−−√ = 9 and 8–√8 = 2.

Since 9 is greater than 2, we can conclude that 81−−√ > 8–√8.

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