How do you simplify (-5+5root4(5))/(3root4(6))−5+54√534√6?

1 Answer
marfre
Aug 8, 2017

(5(root(4)(5) -1))/(3 root(4)(6)) = 5/18(root(4)(5)-1)6^(3/4)5(4√5−1)34√6=518(4√5−1)634

Explanation:

Given: (-5 + 5root(4)(5))/(3 root(4)(6)) −5+54√534√6

To simplify factor a 55 in the numerator: (5(root(4)(5) -1))/(3 root(4)(6))5(4√5−1)34√6

This could be considered a simplified solution, although it is possible to eliminate the denominator knowing that root(4)(6) = 6^(1/4)4√6=614. Multiply both numerator and denominator by 6^(3/4)634:

(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(4√5−1)3⋅614⋅634634=5(4√5−1)6343⋅614⋅634=5(4√5−1)6343⋅6

= 5/18(root(4)(5)-1)6^(3/4)=518(4√5−1)634

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