The absolute value of a real number is defined as the principle square root of the square of a number.

for instance the absolute value of $\mid 4 \mid$ is 4

when a number is between the brackets, it must be brought out of the bracket like this:

$\mid 4 \mid$

$=4^2$

$=\sqrt {16}$

$=4$

Whenever a number is between brackets, the answer must be a positive number. However, after the number is out of the brackets it can become negative in an equation.

We also learned about roots and radicals. Numbers with square roots can never be negative, like $\sqrt {-25}$ because it cannot be calculated and results in an error when put into a calculator. On the other hand, a cubed number can be negative. Roots with an index that’s even cannot be negative, but roots that have an uneven index can be negative.

when simplifying roots that are not perfect, a different approach must be taken.

for example:

$\sqrt {24}$

$=\sqrt {4*6}$ find two multiples of a number, one being a perfect square

$=\sqrt {4} * \sqrt {6}$ separate the roots

$=2 \sqrt {6}$ square the perfect square and leave the radical as a square root

this applies to other index’s as well, just find perfect cubes instead of perfect squares, etc.