Rational Square Roots Lesson 9-3

2 2 2 x 2 = 4

3 x 3 = 9 3 3

4 x 4 =

5 5 5 x 5 = 25

The square root of 4 is 2

The square root of 9 is 3

The square root of 16 is 4

The square root of 25 is 5

You need to memorize at least the first 15 perfect squares.

Square root  1 = 1  4 = 2  9 = 3  16 = 4  25 = 5  36 = 6  49 = 7  64 = 8  81 = 9  100 = 10  121 = 11  144 = 12  169 = 13  196 = 14  225 = 15 Square root

 The is called the radical sign. The number under the radical is called the radicand. In,25 is the radicand. Radical Sign

 1.Simplify if you know the square root. 2.Use the Hockey Stick Method if necessary. Steps

 Factor Tree Method For every pair (square) you pull out 1.

 Hockey Stick For every pair (square) you pull out 1.









Irrational Numbers Irrational numbers cannot be written as a fraction. They are non-terminating, non-repeating decimals. Example: √67

Find two consecutive whole numbers that the given square root is between. (Try to do this without using the table).  18  115  18 is between 4 and 5  115 is between 10 and 11  16 = 4 and  25 = 5 so  100 = 10 and  121 = 11 so

Steps for Simplifying 1. Look for perfect square factors using a factor tree. 2. Pull out all squares 3. Leave factors with no square root under the radical.

For every pair (square) you pull out 1.

Simplified Radical Form  18 =  9 2  = 99 22 3 22 =  108 =  36 3  =  36 33 6 33 =  96 =  16 6  =  16 66 4 66 = No factor inside the radical should be a perfect square.

Irrational Rational

Simplify the following expressions  49 7  4-4   =-2 = =56 + 9= 65  = =25 + 7= 32

Simplify the following expressions =  44  81 =  1 36  – = – = 2 1 – = 1

Pop Quiz!!! Simplify lowest radical