Final answer:
Only statement A is true; it posits that the square root of a positive number greater than 1 is less than the number itself. Statements B, C, and D are false regarding properties of square roots and perfect squares.
Step-by-step explanation:
Let's evaluate each statement regarding square roots step by step:
- A: The square root of a positive number greater than 1 is less than the number. This statement is true. For example, √9 = 3, which is less than 9. The square root of any positive number greater than 1 will always be less than the original number because you are finding a number that, when multiplied by itself, gives the original number, which is a smaller factor.
- B: The square root of a positive number is always less than half of the number itself. This statement is false. Consider the number 4, its square root is 2, which is exactly half. There isn't a rule that states the square root of a number will always be less than half of that number.
- C: The square root of a positive number less than 1 is less than the number. This is false. Actually, the square root of a number less than 1 is greater than the original number. For example, √0.25 = 0.5, which is greater than 0.25.
- D: The square root of a perfect square is not a whole number. This statement is false. A perfect square is a number that is the square of an integer. Hence, its square root will also be an integer, or a whole number, such as the square root of 16 (√16) being 4.
In summary, the only true statement about square roots from the given options is statement A.