SOLUTION: okay so how do i simplify the square root of 128? i know it has something to do with prime numbers i was thinking product rule using 4, 2 and sixteen but i am not sure what to do a

Algebra ->  Square-cubic-other-roots -> SOLUTION: okay so how do i simplify the square root of 128? i know it has something to do with prime numbers i was thinking product rule using 4, 2 and sixteen but i am not sure what to do a      Log On


   

Question 171504: okay so how do i simplify the square root of 128? i know it has something to do with prime numbers i was thinking product rule using 4, 2 and sixteen but i am not sure what to do after that or how to write it!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You started on the right track.

Prime factorization of 128
128/2 = 64
64/2 = 32
32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1

So there are 7 factors of 2 that make 128. Put another way, 128=2%5E7

Also, 2%5E7 can be expressed as 2%2A2%5E6

Therefore sqrt%28128%29=sqrt%282%2A2%5E6%29=2%5E3%2Asqrt%282%29=8%2Asqrt%282%29

Let's see if this answer makes sense:

8%2Asqrt%282%29%2A8%2Asqrt%282%29=64%2A2=128. Yep, that works.