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–√.
Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.(1 point)
The inequality is: 21−−√
17−−√.
To compare the values 21−−√ and 17−−√ using rational approximations, we can simplify them to decimals.
First, approximate 21−−√:
To find a rational approximation for √21, we can find the square root of a number that is close to 21. Let's try 16. The square root of 16 is 4.
Next, evaluate √21 using the approximation:
√21 ≈ √16 + √5 ≈ 4 + √5
Now, approximate 17−−√:
To find a rational approximation for √17, we can find the square root of a number that is close to 17. Let's try 16. The square root of 16 is 4.
Next, evaluate √17 using the approximation:
√17 ≈ √16 + √1 ≈ 4 + 1 = 5
Comparing the two approximations:
4 + √5 < 4 + 1
Simplifying:
√21 < 5
Therefore, the inequality statement comparing 21−−√ and 17−−√ is:
√21 < 5
To compare the values of √21 and √17 using rational approximations, we need to find the closest rational numbers to each square root.
First, let's find the rational approximation for √21:
We know that √16 = 4, so the closest perfect square less than 21 is 16.
Taking the square root of 16, we get √16 = 4.
Now, let's find the rational approximation for √17:
We know that √16 = 4, so the closest perfect square less than 17 is also 16.
Taking the square root of 16, we get √16 = 4.
Comparing the two rational approximations, we have:
4 < 4
Therefore, the inequality statement comparing √21 and √17 is:
√21 < √17