3.4 Radicals.notebook
2015 03 13
March 12, 2015
3.4 Working with Radicals
The word radical refers to any term that includes the symbol √
Typically you have seen square roots, but we will also examine n
cube roots ∛ as well as higher roots √ .
exact value
approximate value
entire radical ­ coefficient of 1 (no number out front of the radical).
mixed radical is a radical that does contain a coefficient.
"3 times the square root of 2"
1
3.4 Radicals.notebook
March 12, 2015
Simplifying Radicals (express as a mixed radical)
In order to simplify radicals, identify any factors of the number that are themselves perfect squares.
Perfect Squares:
Examples
entire radical
mixed radical
2
3.4 Radicals.notebook
March 12, 2015
Converting Mixed Radicals to Entire Radicals
In order to move from a mixed radical to an entire radical, first place the square of the coefficient underneath a square root symbol then multiply the two numbers.
Ex.
Adding & Subtracting Radicals
In order to add radicals they must have the same number underneath the radical symbol (called like radicals).
Ex.
3
3.4 Radicals.notebook
March 12, 2015
Ex. Determine the area and perimeter of the following shape. Leave your answer as a simplified radical.
A=l x w
P=2(l+w)
4
3.4 Radicals.notebook
March 12, 2015
Homework: Pg. 167 #1‐6ad,9,10,12
Quiz Tuesday (after the Break) 3.1 ‐ 3.4
• properties of quadratics from factored form
i.e., vertex, zeros, direction, step pattern, optimal valve, axis of symmetry
• inverse of a quadratic
• simplifying radicals
• completing the square
5