Question

Please, how can find the square root of: ((3+root(5))/2)

Answer 1

it will contain, the root 5 term , right?
so let the square root be
a+b root 5

Answer 2

so we have
\(\sqrt{(3+\sqrt5)/2}=a+b\sqrt5\)
now square both sides, what u get ?

Answer 3

there's another shorter way, of splitting the '3'
but you can first try this :)

Answer 4

^^^ what he said ;D

Answer 5

thanks guys! That is greaaaaaaaat!

Answer 6

hartnn, can you show me the shorter way too please? I did it with the longer method.

Answer 7

\(\sqrt{(3+\sqrt5)/2}=(1/2)\sqrt{6+2\sqrt5}=(1/2)\sqrt{1+5+2\sqrt 5}\)
note that now,quantity under the square root has form \(a^2+b^2+2ab \\ \quad which =(a+b)^2\)
so,
\((1/2)\sqrt{1+5+2\sqrt 5}= (1/2)\sqrt{1^2+(\sqrt5)^2+2*1*\sqrt 5} \\ = (1/2)\sqrt{(1+\sqrt5)^2}=(1/2)(1+\sqrt 5)\)
got it ?

Answer 8

note i split 6 as 1+5

Answer 9

Thanks - yes I have it now. Very nice method!