Using rational approximations, what statement is true? √12 >π

Question

√12<π
√16>4
√16<4

Answer 1

To determine which of the given statements are true, we can evaluate each inequality involving both rational approximations and exact values.

1. √12 > π

   • Calculating √12 gives us approximately 3.464.
   • The value of π is approximately 3.14159.
   • Since 3.464 > 3.14159, this statement is true.

2. √12 < π

   • Since we already established that √12 is approximately 3.464 and π is approximately 3.14159, this statement is false.

3. √16 > 4

   • The value of √16 is exactly 4.
   • Therefore, this statement is false because 4 is not greater than 4.

4. √16 < 4

   • Since we know √16 equals 4, this statement is also false as 4 is not less than 4.

Based on the evaluations:

• √12 > π is true.
• All other statements are false.

So the true statement is: √12 > π.