Using rational approximations, what is an inequality statement comparing √21 and √17? Enter <,>, or =.
√21 ≈ 4.583 and √17 ≈ 4.123.
Therefore, √21 > √17.
Using rational approximations, what is an inequality statement comparing pi and √8? Enter <,>, or =.
π ≈ 3.14159 and √8 ≈ 2.82843.
Therefore, π > √8.
To compare √21 and √17 using rational approximations, we can use the fact that √21 ≈ 4.5826 and √17 ≈ 4.1231.
Comparing these values, we can see that 4.5826 > 4.1231.
Therefore, the inequality statement is √21 > √17.
To compare the square roots √21 and √17 using rational approximations, we can find the closest rational numbers to each square root.
First, let's find the rational approximation for √21. We can start by identifying perfect squares that are close to 21. The perfect squares closest to 21 are 16 (4^2) and 25 (5^2). Since 21 is between these two perfect squares, we know that the approximate value of √21 will be between 4 and 5.
To get a more accurate rational approximation, we can calculate the square root of 21 using a calculator or by long division. The square root of 21 is approximately 4.5826. Therefore, we can say that √21 is roughly equal to 4.5826.
Next, let's find the rational approximation for √17. Just like above, we can identify perfect squares close to 17. The perfect squares closest to 17 are 16 (4^2) and 25 (5^2). Since 17 is closer to 16, we know that the approximate value of √17 will be less than √16 (which is 4) but greater than √9 (which is 3).
To get a more accurate rational approximation, we can calculate the square root of 17 using a calculator or by long division. The square root of 17 is approximately 4.1231. Therefore, we can say that √17 is roughly equal to 4.1231.
Comparing the rational approximations, we have √21 ≈ 4.5826 and √17 ≈ 4.1231. Using the inequality symbols <, >, or =, we can say that √21 > √17.