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.
Question
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: √81 √88
.
Question
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
To compare the values 81−−√ and 8–√8 using rational approximations, we can simplify both expressions.
To start, we can find the rational approximation for 81−−√:
√81 = 9
So, 81−−√ is approximately equal to 9.
Next, we find the rational approximation for 8–√8:
√8 ≈ 2.828
So, 8–√8 is approximately equal to 8 - 2.828 ≈ 5.172.
Comparing the two values, we have:
9 > 5.172
Therefore, the inequality statement is:
81−−√ > 8–√8
To compare the expressions 81−−√ and 8–√8 using rational approximations, we can simplify both expressions to decimal values and then compare them.
First, let's find the decimal value of 81−−√. Using a calculator, we can approximate the square root of 81 as 9. Thus, 81−−√ ≈ 9.
Next, let's find the decimal value of 8–√8. We can simplify 8–√8 by rationalizing the denominator. Multiplying both the numerator and denominator by the conjugate of the denominator (√8 + √8) yields:
8–√8 = (8–√8)(√8 + √8)/(√8 + √8)
= (8√8 + 8 - 8)/(√8 + √8)
= 8√8/(2√8)
= 4
Therefore, 8–√8 = 4.
Now we can compare the decimal values:
9 > 4
So, the inequality statement comparing 81−−√ and 8–√8 is:
81−−√ > 8–√8