how do we multiply and divide radical expression

multiplying and dividing radical expressions can be a challenge but here are two methods that may be very useful.lets multiply first. example 1. √3(√10*√5)

1. √3(√11*√6) we must distribute  √3 to the other two numbers we will get
     √33*√18
2. we and √33*√18 and get √594
3. we got to simplify the radical expression √594 in two numbers...
   I chose √9, √66
4. the same thing to both √9 and √66
   9 is a perfect square  so it will just turn in to 3
   66 is spited in to 6 and 11 
5. we could split 6 in to 2,3 but their is no perfect square her so we could just leave it as √66
6. at the end we are felted with 3√66 as a simplified number 

 Next we will divide √12 / √3

1. we can rewrite this scary looking √12 / √3 in to √12/3 that looks a lot less scary
2. we just divide 12/3 and get √4 the 4 is a perfect square so we still have to simply it
3. and end up with 2 as our final answer  

the numbers that are perfect squares are
√4 √9 √16 √25 √36 √49 √64 etc.
 2  3  4   5   6   7   8 etc.
 
so for more help check out the links below:

• http://www.youtube.com/watch?v=w4r8jjUfouU
• http://www.youtube.com/watch?v=YWtw-pWFGvE
• http://www.purplemath.com/modules/radicals4.htm

How do we simplify radical

simplifying radicals isn't that hard if you know your square root s and our x^2. I'll give you guys an example simplify the square root of 72. we can use my favorite method the factor tree method it is simple and easy.

1. first we got to find two factors that multiply to 72...
   my two factors are 9,8 
2. we do the same with 8,9
   we split 8 in 2,4
   and we split 9 in 3,3
3. we do this one more time to the 4 because we want to have all prime numbers and we get two 2 
4. now we list our prime numbers to make it easier
   72: 3,3,2,2,2
5. we have two pairs of numbers which are the 3's and 2's and we are left with one 2 now we have the square root 3^2 , the square root of 2^2 and the square root of 2 
6. we simplify the 3^2 and 2^2and get  3*2to the square root of 2
   which is simplify to 6 square root of 2

if I confused you or you just want  more help check out the links below:

• http://www.youtube.com/watch?v=PXdYQqjHAuE
• http://www.themathpage.com/alg/simplify-radicals.htm