lsugano
why does the reciprocal of (2√5)/5 equals √5/2 ???



This Question is Closed

hartnn
Best Response
You've already chosen the best response.
1
because \(\huge \frac{\sqrt 5}{5}=\frac{\sqrt 5}{\sqrt5.\sqrt 5}=\frac{1}{\sqrt 5}\)

lsugano
Best Response
You've already chosen the best response.
0
i still dont get it..><

hartnn
Best Response
You've already chosen the best response.
1
\(\huge \frac{2\sqrt 5}{5}=\frac{2\sqrt 5}{\sqrt5.\sqrt 5}=\frac{2}{\sqrt 5}\)
which step ?

Asad0000
Best Response
You've already chosen the best response.
0
(2√5)/5 can also be written as \[\frac{ 2 }{ \sqrt{5} }\]

hartnn
Best Response
You've already chosen the best response.
1
reciprocal means inversing the ratio,
a/b becomes b/a

lsugano
Best Response
You've already chosen the best response.
0
why is the denominator √5 multiply by √5

hartnn
Best Response
You've already chosen the best response.
1
any number can be expressed as
\(a=\sqrt a.\sqrt a\)

hartnn
Best Response
You've already chosen the best response.
1
\(x^m.x^n=x^{m+n} \\so, \huge \sqrt 5.\sqrt 5= 5^{1/2}.5^{1/2}=5^{1/2+1/2}=5^1\)

hartnn
Best Response
You've already chosen the best response.
1
doubts ?

lsugano
Best Response
You've already chosen the best response.
0
wait basically....√5 and 5 is the same?

hartnn
Best Response
You've already chosen the best response.
1
no.... 5 and \(\sqrt 5.\sqrt 5\) are same.

lsugano
Best Response
You've already chosen the best response.
0
but why do we have to multply by √5??

lsugano
Best Response
You've already chosen the best response.
0
OMG i think i got it!!

hartnn
Best Response
You've already chosen the best response.
1
i am glad!

lsugano
Best Response
You've already chosen the best response.
0
so first, the reciprocal of (2√5)/5 is 5/2√5

lsugano
Best Response
You've already chosen the best response.
0
but 5 = √5 . √5

hartnn
Best Response
You've already chosen the best response.
1
es, you can do that way also!

lsugano
Best Response
You've already chosen the best response.
0
and √5 crosses out which equals. √5 / 2!!

lsugano
Best Response
You've already chosen the best response.
0
thank you soooo much!!!! im sorry if i put some streess on you!! i am really bad at math ><

hartnn
Best Response
You've already chosen the best response.
1
no problem at all :)
welcome ^_^