Why is square root of x squared = absolute x?
Is it because absolute x = -x and x?
Wellt the so calles abs: R -> R^+_0 function assigns every x its absolute value hence a positive number or zero.
Squaring a number always yields s.th. positive as a result. It follows the statement.
Yes, since (-x)^2 or x^2 both yield x^2, the square root of X^2 = IxI = absolute value of x.
To understand why the square root of x squared is equal to the absolute value of x (|x|), let's break down the logic step by step.
First, let's examine the expression √(x^2). This expression represents the square root of x squared.
By definition, the square root (√) of a number x represents the value that, when multiplied by itself, equals x. In other words, (√x)^2 = x.
Now, let's consider x^2. This expression represents x multiplied by itself: x * x.
Now, if we take the square root of x^2 (√(x^2)), we want to find the number that, when multiplied by itself, equals x^2.
We know that x^2 is always positive (since multiplying any number by itself always results in a positive value or zero). Therefore, the square root of x^2 (√(x^2)) can't be negative.
The absolute value of x (|x|) takes any value x and makes it positive or zero. It disregards the negative sign if x is negative and keeps x unchanged if it's positive.
So, when we evaluate the expression √(x^2), it gives us the positive square root of x^2. This positive square root is equal to |x|. Therefore, we can conclude that √(x^2) = |x|.