moomoomath logo header
lime green horizontal line
Welcome to MooMooMath
Quick Math Homework Help
Perfect Squares
Radicals (square roots)

√4 = 2
√9 = 3
√16 = 4
√25 =5
√36 =6
√49 = 7
√64 =8
√81 =9
√100 =10

Your radical is in it's simplest form when the radicand cannot be divided evenly by a perfect square.

radical symbol
radical symbolradical symbolradical symbol
radical symbol
video tutorial simplyfing radicals
header simplifying radicals
header simplifying radicalsheader simplifying radicalsheader simplifying radicals
header simplifying radicals
Radicals ( or roots ) are the opposite of exponents. For instance, 3 squared equals 9, but if you take the square root of nine it is 3.
For example
4^2=16 and √16 =4 
2^3=8 and ∛8 = 2 
3^3= 27 and ∛27=3 

The check mark √ is called the radical symbol and gives you three pieces of important information, the degree, the radical symbol, and the radicand.

The Degree is the number of times the number ( called the radicand) has been multiplied by itself. 

A degree of 3 is a cube root, a 4 is the fourth root. Most times for a square root a degree will be missing, and it is assumed that it is a square root.









Method 1. Find the largest perfect square that will divide into the radical

Simplify √32  

Step 1 Find the largest perfect square that will divide evenly into 32
  16 * 2 =32

Step 2 Write these numbers under the radical √(16*2)

Step 3 Give each number it’s own radical sign √16*√2 

Step 4 “Take out” or reduce the perfect square 4√2 ( perfect square of 16=4)


Simplify √75 
25*3 =75  Step 1. Find largest perfect square

√(25*3)    Step 2. Write the numbers under the radical.

√25*√3    Step 3. Give the numbers a radical sign.

5√3           Step. 4. Take out any perfect squares (square of 25=5)

Method 2  Simplify a radical " Jailbreak Method"
I have taught this method to my students for many years it it helps many remember the steps of simplifying
Simplify √75 

Step 1 Create a factor tree



​Step 2 When the radical is a square root any like pair of numbers escape from under the radical. In this example the pair of 5’s escape and the 3 remains under the radical.
 √(5 5 3) the 5’s jailbreak and escape in a pair and the three remains under the radical
5√3 

Simplify √96  

Step 1. Draw a factor tree

factor tree of 96
Step 2 Pairs of like numbers escape In this example you have 2 pairs of 2

Step 3 Multiply the pairs together 2*2 = 4√(2 3)

Step 4 Multiply the numbers remaining under the radical 2*3 = 6

Step 5 therefore √(96 )=4√6

table
a line
a line

How to simplify radicals

Simplifying Radicals “ Square Roots”

In order to simplify a square root you take out anything that is a perfect square.

Being familiar with the following list of perfect squares will help when simplifying radicals
the degree of a radical

Radicand The value that you are taking the root of.

the radicand of a radical in math
Radical symbol. The symbol that looks like a check mark. √ The bar tells you how much of the value to use. You can think of the bar as parenthesis. For example​,


cube root of 30-3
The bar is over 30 -3 so subtract 30 -3 =27,then take the square root.
cube root of 27 -2
The bar is only over the 27 so take the cube root of 27 which equals 3 then subtract 2 
Perfect Squares

4 = 2x2
9= 3x3
16= 4x4
25= 5 x5
36= 6x6
49= 7x7
64= 8x8
81= 9x9
100=10 x 10