which of following statements is false
1. The absolute value of a real number is the principal square root of the square of the number.
2. The absolute value of a real number is the distance of the number from zero on a number line.
3. The absolute value of a real number can never be negative.
I thought it be statement 2, and 3 but it also number 1, and i not real understand what that statement means.
The false statement among the three is statement 3 - "The absolute value of a real number can never be negative." This statement is false because the absolute value of a real number is always non-negative (greater than or equal to zero), but it can equal zero. The absolute value of a number represents its distance from zero on a number line.
To determine which statement is false, let's examine each statement one by one:
Statement 1: "The absolute value of a real number is the principal square root of the square of the number."
To understand this statement, we need to understand what the absolute value of a number is. The absolute value of a real number is simply the positive value of that number, regardless of its sign. For example, the absolute value of -5 is 5.
The statement is saying that the absolute value of a real number is equal to the principal square root of the square of that number. The principal square root √ is the positive square root of a number.
To verify if this statement is true, we can take a real number, square it, then find the principal square root of the result and compare it with the absolute value of the original number.
For example, let's take the number -3. The square of -3 is 9, and the principal square root of 9 is 3. The absolute value of -3 is also 3. So, in this case, the statement is indeed true.
Statement 2: "The absolute value of a real number is the distance of the number from zero on a number line."
This statement is true. The absolute value of a real number can be thought of as the distance of that number from zero on a number line. For example, the absolute value of -5 is 5, which is the distance between -5 and 0.
Statement 3: "The absolute value of a real number can never be negative."
This statement is also true. The absolute value of a real number is always positive or zero. It represents the magnitude of the number without considering its sign.
Therefore, from our analysis, the false statement is Statement 1. The absolute value of a real number is not necessarily equal to the principal square root of the square of the number.
#1 is false , all we need is one counterexample
Assume the statement is true.
| 64 | = 64
√64 = 8
64≠ 8