Final answer:
The statement that is not true among the options provided is c) √27 + 3 > 17, because the square root of 27 is slightly greater than 5, and adding 3 to it does not result in a number greater than 17.
Step-by-step explanation:
To determine which of the following statements is not true, we must evaluate each one:
- a) √16 + 4 > √4 + 5: Simplifying √16 gives us 4, so this is equivalent to 4 + 4 > 2 + 5, which simplifies to 8 > 7. This is true.
- b) 2a > 9: Without knowing the value of a, this cannot be evaluated. It could be true or false depending on the value of a.
- c) √27 + 3 > 17: Simplifying √27 gives a value greater than 5 (since 5^2 = 25 and the square root of 27 is slightly more), so adding 3 will give us something greater than 8 which is not greater than 17. This statement is not true.
- d) 5 - √24 < 1: Simplifying √24 gives a value less than 5 (since 4^2 = 16 and the square root of 24 is between 4 and 5), so 5 - a number less than 5 will result in a value greater than 0 but less than 1. This statement is true.
Therefore, the statement that is not true is: c) √27 + 3 > 17.