Using rational approximations, what statement is true?
√12 < Π
√12 > Π
√16 < 4
√16 > 4
√12 > Π
can i have an explanation?
Sure!
To determine the correct statement, we need to compare the values of √12 and Π (pi). We can approximate √12 and Π using rational approximations to make the comparison easier.
For √12, we can approximate it using the fact that √9 = 3 and √16 = 4. Since 12 is between 9 and 16, we can estimate that √12 is between 3 and 4.
Next, let's approximate Π. We can use the rational approximation of Π as 3.14 or 22/7 to make the comparison easier.
Since 3 < 3.14 and 4 > 3.14, we can conclude that √12 > Π. Therefore, the correct statement is √12 > Π.
The correct statement is √16 = 4.
To determine which of the given statements are true, we can use rational approximations to compare the values.
First, let's consider √12 and Π. Rational approximations for √12 and Π are √12 ≈ 3.46 and Π ≈ 3.14. From this, we can see that √12 > Π. Therefore, the statement √12 > Π is true.
Next, let's consider √16 and 4. Rational approximations for √16 and 4 are √16 = 4 and 4 = 4. Since 4 is equal to √16, the statement √16 = 4 is true.
In summary, the true statements among the given options are √12 > Π and √16 = 4.
To determine which statement is true using rational approximations, we can approximate the values of √12, √16, and π.
Let's start by approximating √12:
√12 can be written as √(4 × 3), which is equal to √4 × √3, or 2√3. Since √3 is an irrational number, we can estimate its value using rational approximations. Taking √3 ≈ 1.7 (rounded to one decimal place), we can find that √12 is approximately 2 × 1.7 = 3.4.
Next, let's approximate √16:
√16 is equal to 4, as 4 squared is equal to 16.
Lastly, let's approximate π:
π is a transcendental number and is not rational. However, we can use an approximate value of π to compare with the other values. Taking π ≈ 3.14 (rounded to two decimal places) is a commonly used approximation.
Now let's compare the approximations:
√12 ≈ 3.4
π ≈ 3.14
√16 = 4
From the given options, we can now determine which statement is true:
√12 > π (3.4 > 3.14)
√12 > √16 (3.4 > 4)
Therefore, the statement √12 > √16 is true.