Question

The absolute value of | | is equal to the square root of __________.

Option 1: The original number
Option 2: The square of the original number
Option 3: The cube of the original number
Option 4: The reciprocal of the original number

Answer 1

The absolute value of a number is equal to the square root of the square of the original number. This represents the non-negative value of that number, irrespective of its sign.

Step-by-step explanation:

The absolute value of a number is the non-negative value of that number without regard to its sign. Therefore, the absolute value of a number is equal to the square root of the square of the original number. To explain further, if we have a number x, and we square it to get x², the absolute value of x is the square root of x², which brings us back to the original number x, but without any sign (positive or negative).

For instance, if we consider the number 5 and square it, we get 25. Taking the square root of 25 gives us back the number 5, which is the absolute value of both 5 and -5. Similarly, for a negative number like -4, squaring it gives us 16, and the square root of 16 is 4, which represents the absolute value of -4.

In algebra, we frequently encounter equations where we have to square a number and then find the square root to simplify the expression or to isolate a variable. Knowing the relationship between squaring a number and taking the square root is essential for solving such equations.