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