SOLUTION: I do not know how to simplify this radical expression: The first has a 5 inside the radical and these are the numbers and variables inside the root---> 192t^17u^15 It must be

Algebra ->  Radicals -> SOLUTION: I do not know how to simplify this radical expression: The first has a 5 inside the radical and these are the numbers and variables inside the root---> 192t^17u^15 It must be      Log On


   

Question 747110: I do not know how to simplify this radical expression:
The first has a 5 inside the radical and these are the numbers and variables inside the root---> 192t^17u^15
It must be simplified as much as possible
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
root%285%2C192t%5E17u%5E15%29

Write 192 = 26·3

root%285%2C2%5E6%2A3%2At%5E17u%5E15%29

Write each exponent in terms of the largest
multiple of the index of the radical which
does not exceed it.

Looking at the 26, the largest multiple of index
5 that does not exceed 6 is 5. So we write 26 as 25+1 = 25·21·

root%285%2C2%5E%285%2B1%29%2A3%2At%5E17u%5E15%29 

Looking at the t17, the largest multiple of index
5 that does not exceed 17 is 15. So we write t17 as t15+2 = t15t2·

root%285%2C2%5E%285%2B1%29%2A3%2At%5E%2815%2B2%29u%5E15%29

Looking at the u15, this exponent is already a multiple of index
5 so we leave it as it.

We use the identity ab+c =abac to
rewrite  

25+1 = 2521 = 25·2,

and 

t15+2 = t15+2 = t15t2

root%285%2C2%5E5%2A2%2A3%2At%5E15t%5E2u%5E15%29 

To take the factors with exponents which are multiples of 5,
out of the radical, divide their exponent by the index 5, 
and get:

2%2At%5E3%2Au%5E3%2Aroot%285%2C2%2A3%2At%5E2%29

2t%5E3u%5E3%2Aroot%285%2C6t%5E2%29

Edwin