how do i similify a nonperfect radical expression?

Question

I do not understand this

Answer 1

Do you have a specific problem?

Answer 2

You first write down the radiant ( the number under radical ) as product of its prime facors.

 

  Fundamental law of Arithmetic says that : Every Composite number consists of product of its prime factors:

 

 

      4 = 2. 2 = 2²

 

      6 = 2 . 3 

   

       8 = 2.2 2 = 8

 

      10 = 2 . 5

 

      12 = 2 . 2 .3 = 2² . 3

   

       14  = 2 . 7

 

      16  = 2 ⁴    

      

      18 = 2  . 3²

  

      20   =  2² . 5 

 

      We can multiply and divide the radicals, where the product and quotient to be a radical with product and quotient to be the product and quotient of the radicants  of radicants .

 

 

     √a . √b  = √(ab)  ,         √a / √b = √(a/b) .

 

 

     To simplify:   √(a²b ) = √a² . √b = a √b

 

          So To Simplify:

 

            √12  = √( 2². 3 = 2 √3

 

             √18 = √( 2 . 3²) = 3√2

 

            √(20) = √( 2² . 5 ) = 2 √5

            

            √24 = √(2² . 6 ) = 2 √6

     

            √28 = √2² .7 = 2 √7