5-5 ROOTS OF REAL NUMBERS Objective: Students will be able to simplify radicals.
Terminology Index: tells us what root we are looking for Radicand: term underneath the radical sign
To Find the ROOT of a VARIABLE… divide the exponent on the variable by the index. Examples:
Find the roots of each of the following: 1) 2)3) 4)5)6)
COMMON ROOTS
5-6 RADICAL EXPRESSIONS Objectives Students will be able to: 1) Simplify radical expressions 2) Add, subtract, multiply, and divide radical expressions
Steps to simplify a square root. 1) Factor the radicand into as many squares as possible. 2) Isolate the perfect square terms. 3) Simplify each radical.
Example 1: Simplify each expression. 1)2) 3)4)
Try these. 4)5)
Adding and subtracting radicals is very similar to adding and subtracting monomials. Remember, to add or subtract monomials, you need the same variables and same exponents on those variables (like terms). To add or subtract radical expressions, you need the same radicand and same index (like radical expressions) If the terms have the same radicand and same index, you add/subtract the terms on the outside of the radical expression, and keep the index and radicand. You may need to simplify the terms before you can add/subtract.
Example 2: Simplify. 1)2) 3)4)
Try these: 5)6)
When multiplying radical expressions, the terms on the outside of the radicals are multiplied, and the radicands are multiplied. You then simplify, if possible. If you choose, you can simplify the radical expressions first (if possible), and then multiply. EXAMPLE TIME!!!
Example 3: Simplify. 1)2) 3)4)
Try these. 5)6)
7) 8)
9)
Try these. 10) 11)
There can never be a radical in the denominator of a fraction. If a denominator contains a radical, the expression must be rationalized. This occurs by multiplying the entire expression by a form of the number 1. The goal is to multiply by a quantity so that the radicand has an exact root. Let’s see what this all means…
Example 4: Simplify. 1) 2) 3)4)
5)6) Try these. 7)8)
9) 10)
Try this. 11)