# Week 3 – Precalc 11

For week 3 of pre-calc 11, we had two short lessons to begin our unit on “Absolute Value and Radicals”. Lesson 1 focused on absolute value, something I had not been familiar with until now. The concept describes the digit value of a number from zero. A formula can be used in which you take the square root of a square to get a numbers absolute value.

Ex: $\sqrt{x^2}$

If we take the number -5 for example, -5 squared is 25, then root 25 is 5. The absolute value of -5 is 5. It is 5 places away from 0.

$\sqrt{(-5)^2}$ = 5

Lesson 2 focused on simplifying radical expressions, using the prime factorization and breaking down the expression, methods that we used in math 10. To simplify an entire radical such as $\sqrt{96}$ we take all the prime factors (2x2x2x2x2x3), and gather the groups of 2 as it is a SQUARE root. There are two groups of 2’s with a leftover 2 and a leftover 3. The groups are multiplied together (2×2 = 4) which makes the coefficient, and the leftovers are multiplied giving the radicand. $\sqrt{96}$ = 4$\sqrt{6}$