Adding Radicals

Question

-5√48 + 4√108

Answer 1

To add radicals, they must have the same radicand (expression under the radical).  Let's try to simplify each radicand:

 

     -5√48 + 4√108

 

     = -5√(16*3) + 4√(36*3)

     = -5√(4²*3) + 4√(6²*3)

Now √4² = 4 and √6² = 6 so we can take those outside of the radical:

 

     = -5*4√3 + 4*6√3

     = -20√3 + 24√3

 

     = 4√3

Answer 2

Hi Taylor-

I assume that you are trying to reduce this expression to its lowest, common terms.

Start by breaking down the term under the radical:

-5√48 = -5√16x3 = -5x4√3 = -20√3

4√108 = 4√36x3 = 4x6√3 = 24√3

Now add the reduced values of these terms together:

-20√3 + 24√3 = 4√3

 

Hope that helps.