Processing math: 100%
 
+0  
 
0
12
2
avatar+21 

Simplify 4133+39

 Oct 10, 2024
 #1
avatar+1208 
0

That simplifies to 2*3^(1/3).  Hope this helps!

 Oct 10, 2024
 #2
avatar+189 
0

Whenever there are multiple radical terms in the denominator, the process of simplification becomes quite a challenge, but I realized after some time that the denominator 133+39=(33)233+1 looks to take the form of the beginnings of the factorization of the sum of cubes.

 

In the general factorization, a3+b3=(a+b)(a2ab+b2). If we consider the case where a=33 and b=1, then we can multiply the denominator by 33+1 to transform the denominator into a sum of cubes and then simplify. 

 

4133+3933+133+1=4(33+1)(33)3+13=4(33+1)3+1=33+1

 Oct 13, 2024

0 Online Users