simplify-2-5-1-3-

Question Number 160831 by MathsFan last updated on 07/Dec/21

simplify \sqrt[3]{2 + \sqrt{5}}

Commented by mr W last updated on 07/Dec/21

\sqrt[3]{2 + \sqrt{5}}

= \frac{\sqrt[3]{16 + 8 \sqrt{5}}}{2}

= \frac{\sqrt[3]{5 \sqrt{5} + 3 \sqrt{5} + 3 \times 5 + 1}}{2}

= \frac{\sqrt[3]{{(\sqrt{5})}^{3} + 3 {(\sqrt{5})}^{2} + 3 \sqrt{5} + 1}}{2}

= \frac{\sqrt[3]{{(\sqrt{5} + 1)}^{3}}}{2}

= \frac{\sqrt{5} + 1}{2} = ϕ = g o l d e n r a t i o

Commented by MathsFan last updated on 08/Dec/21

t h a n k y o u s i r

b u t i s t h e r e a n y f o r m u l a f o r

q u e s t i o n s l i k e t h i s p l e a s e ?

Commented by mr W last updated on 08/Dec/21

n o! o n e k n o w s i t o r o n e {d o e s n}^{'} t k n o w

i t . t h e r e i s n o g e n e r a l w a y t o s o l v e i t

t h r o u g h a f o r m u l a!

Commented by MathsFan last updated on 08/Dec/21

o k a y S i r .

T h a n k y o u o n c e a g a i n