“The absolute value of a real number is defined as the principal square root of the square of number.” Which means the absolute value of a real number is the square root of a squared number. The absolute value of a number is its distance from zero (0) on a number line. This ignores the “+” or “-” sign of a number, because distance in math is never negative. Every real number can be represented as a point on a number line.

The absolute value of -4 is |-4|=4

We can prove this by squaring 4 then square rooting it. After continuously doing this you realize that the answer is always the number inside the modulus (except it is always positive). Another way of looking at it is that the square and the square root cancel each other out.

REMEMBER!

If there’s an equation is in the modulus, you must solve before finding the absolute value.

Ex.

|-8+3|=|-5|

=5