1.1 S IMPLIFYING R ADICALS Sec Math 2
S IMPLIFYING R ADICALS
Methods for Simplifying Radical Expressions Two Methods for Simplifying Radical Expressions: 1. Simplify by finding perfect squares 2. Simplify by creating a factor tree
1. Simplify by finding perfect squares
P ERFECT S QUARES
= 2 = 4 = 5 = 10 = 12
= = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM
= = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM
2. Simplify by creating a factor tree
Step 1. Factor the number under the radical sign into prime numbers 48 = 2 ∙ 24 2 ∙ 12 2 ∙ 6 2 ∙ 3 Prime numbers of 48 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 Simplify or Reduce a Radical by Finding Prime Factors Reduce
Step 2. Group prime numbers into squares Step 3. Reduce the radical from the perfect squares Step 4. Simplify the radical. Simplify or Reduce a Radical by Finding Prime Factors
Simplify Each Expression Simplify Method 1: Finding Perfect Squares Method 2: Factor into Prime Numbers
A radical expression is in simplest form when all the following are true.
Simplify or Reduce a Radical Simplify the expression
= X = Y 3 = P 2 X 3 Y = 2X 2 Y = 5C 4 D 10
= = = =
= = = =
Please Do you homework Worksheet: 1.1 Simplifying Radicals