# Week 3 Absolute Value and Simplifying Radical Expressions

This week in Pre Calculus 11, we learned what an absolute value of a real number was and how to simplify radical expressions.

Absolute Value of a Real Number : The principal square root of a square number.

SOLUTION: The absolute value of a negative number is the opposite number, and the absolute value of a positive number and 0 are the same.

ex/    |-99| = 99         | 12 | = 12

This is because distance is always positive.

The long lines act as brackets but are not and it represents absolute value.

• ex 1/         4 |15-20|
•                     4 |-5|
•                     4 (5)
•                     = 20

• ex 2/         |6 +(-10)| -|5-7|
•                     |6-10| – | -2|
•                     |-4| – |2|
•                     4  –   2
•                     = 2

Here is a video that really helped me learn and understand a little bit more about absolute value.

we also briefly reviewed radical expressions

ex/ $\sqrt{25}$ =   5  and $3\sqrt[2]{5}$ = $\sqrt{45}$

Solving

Step 1: Find perfect squares.

Step 2: Take them out / simplify

Step 3: Do the same with the variables (treat them like numbers)

ex/ $\sqrt[2]{18x}$

• ex/ $\sqrt[2]{18x^2}$
• $\sqrt{9\cdot{x^2}\cdot2}$
• $\sqrt{3\cdot3\cdot{x}\cdot{x}\cdot2}$
• $3x\sqrt[2]{2}$

This is how to work with variables in Radical Expressions