How do you simplify #(-5+5root4(5))/(3root4(6))#?

1 Answer
Aug 8, 2017

Answer:

#(5(root(4)(5) -1))/(3 root(4)(6)) = 5/18(root(4)(5)-1)6^(3/4)#

Explanation:

Given: #(-5 + 5root(4)(5))/(3 root(4)(6)) #

To simplify factor a #5# in the numerator: #(5(root(4)(5) -1))/(3 root(4)(6))#

This could be considered a simplified solution, although it is possible to eliminate the denominator knowing that #root(4)(6) = 6^(1/4)#. Multiply both numerator and denominator by #6^(3/4)#:

#(5(root(4)(5) -1))/(3 * 6^(1/4)) * (6^(3/4))/(6^(3/4)) = (5(root(4)(5) -1)6^(3/4))/(3 * 6^(1/4) * 6^(3/4)) = (5(root(4)(5) -1)6^(3/4))/(3 * 6) #

#= 5/18(root(4)(5)-1)6^(3/4)#