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

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because \(\huge \frac{\sqrt 5}{5}=\frac{\sqrt 5}{\sqrt5.\sqrt 5}=\frac{1}{\sqrt 5}\)
i still dont get it..><
\(\huge \frac{2\sqrt 5}{5}=\frac{2\sqrt 5}{\sqrt5.\sqrt 5}=\frac{2}{\sqrt 5}\) which step ?

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Other answers:

(2√5)/5 can also be written as \[\frac{ 2 }{ \sqrt{5} }\]
reciprocal means inversing the ratio, a/b becomes b/a
why is the denominator √5 multiply by √5
any number can be expressed as \(a=\sqrt a.\sqrt a\)
\(x^m.x^n=x^{m+n} \\so, \huge \sqrt 5.\sqrt 5= 5^{1/2}.5^{1/2}=5^{1/2+1/2}=5^1\)
doubts ?
wait basically....√5 and 5 is the same?
no.... 5 and \(\sqrt 5.\sqrt 5\) are same.
but why do we have to multply by √5??
OMG i think i got it!!
i am glad!
so first, the reciprocal of (2√5)/5 is 5/2√5
but 5 = √5 . √5
es, you can do that way also!
and √5 crosses out which equals. √5 / 2!!
thank you soooo much!!!! im sorry if i put some streess on you!! i am really bad at math ><
no problem at all :) welcome ^_^

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