*need asap! *
why are radicals simplified before adding and subtracting? explain your reasoning by adding sqrt8 and sqrt32 algebraically. compare the process to multiplying and dividing.

They are simplified in hopes of finding like terms so we can add or subtract them.

When multiplying or dividing we can multiply or divide the numbers under the radicals before simplifying

Step-by-step explanation:

√8 and √32 are not like terms, so we can't simply add or subtract them.  We first want to reduce them down as much as possible...

√8 + √32  

   √8 = (√4)(√2) = 2√2

       √32 = (√16)(√2) = 4√2

So √8 + √32 is the same as 2√2 + 4√2  

These are now like terms since they share a common number under the radical sign.  

2√2 + 4√2 = 6√2

Multiplying:   (√2)(√2) = √4 = 2

Dividing:  (√16)/(√4) = √4 = 2

                or   (√16)/(√4) = 4/2 = 2