Find a rational number between 𝝅 and √12. Show your work.
To find a rational number between π and √12, we can convert both numbers into rational approximations.
First, let's consider π. We know that π is approximately equal to 3.14159. Since π is between 3 and 4, we can say that 3 < π < 4.
Next, let's consider √12. To find a rational approximation for √12, we can simplify the square root expression as much as possible. √12 can be written as √(4*3), which can be further simplified as √4 * √3. Since √4 = 2, we have 2√3.
To find another rational approximation, we can approximate √3. We know that √3 is between 1 and 2, so we can say that 1 < √3 < 2.
Therefore, we have:
3 < π < 4
1 < √3 < 2
To find a rational number between these two ranges, we can use the following approximation:
3 < π < 4
1 < √3 < 2
Taking the rational number 3.2, we have:
3 < 3.2 < π < 4
1 < √3 < 2
Thus, 3.2 is a rational number between π and √12.
what is going on here ? pls explain
Taking the rational number 3.2, we have:
3 < 3.2 < π < 4
1 < √3 < 2