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lsugano

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

  • one year ago
  • one year ago

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  1. hartnn
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    because \(\huge \frac{\sqrt 5}{5}=\frac{\sqrt 5}{\sqrt5.\sqrt 5}=\frac{1}{\sqrt 5}\)

    • one year ago
  2. lsugano
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    i still dont get it..><

    • one year ago
  3. hartnn
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    \(\huge \frac{2\sqrt 5}{5}=\frac{2\sqrt 5}{\sqrt5.\sqrt 5}=\frac{2}{\sqrt 5}\) which step ?

    • one year ago
  4. Asad0000
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    (2√5)/5 can also be written as \[\frac{ 2 }{ \sqrt{5} }\]

    • one year ago
  5. hartnn
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    reciprocal means inversing the ratio, a/b becomes b/a

    • one year ago
  6. lsugano
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    why is the denominator √5 multiply by √5

    • one year ago
  7. hartnn
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    any number can be expressed as \(a=\sqrt a.\sqrt a\)

    • one year ago
  8. hartnn
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    \(x^m.x^n=x^{m+n} \\so, \huge \sqrt 5.\sqrt 5= 5^{1/2}.5^{1/2}=5^{1/2+1/2}=5^1\)

    • one year ago
  9. hartnn
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    doubts ?

    • one year ago
  10. lsugano
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    wait basically....√5 and 5 is the same?

    • one year ago
  11. hartnn
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    no.... 5 and \(\sqrt 5.\sqrt 5\) are same.

    • one year ago
  12. lsugano
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    but why do we have to multply by √5??

    • one year ago
  13. lsugano
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    OMG i think i got it!!

    • one year ago
  14. hartnn
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    i am glad!

    • one year ago
  15. lsugano
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    so first, the reciprocal of (2√5)/5 is 5/2√5

    • one year ago
  16. lsugano
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    but 5 = √5 . √5

    • one year ago
  17. hartnn
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    es, you can do that way also!

    • one year ago
  18. lsugano
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    and √5 crosses out which equals. √5 / 2!!

    • one year ago
  19. lsugano
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    thank you soooo much!!!! im sorry if i put some streess on you!! i am really bad at math ><

    • one year ago
  20. hartnn
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    no problem at all :) welcome ^_^

    • one year ago
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