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lsugano

  • 2 years ago

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

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  1. hartnn
    • 2 years ago
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    because \(\huge \frac{\sqrt 5}{5}=\frac{\sqrt 5}{\sqrt5.\sqrt 5}=\frac{1}{\sqrt 5}\)

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

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

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

  5. hartnn
    • 2 years ago
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    reciprocal means inversing the ratio, a/b becomes b/a

  6. lsugano
    • 2 years ago
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    why is the denominator √5 multiply by √5

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

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

  9. hartnn
    • 2 years ago
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    doubts ?

  10. lsugano
    • 2 years ago
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    wait basically....√5 and 5 is the same?

  11. hartnn
    • 2 years ago
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    no.... 5 and \(\sqrt 5.\sqrt 5\) are same.

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

  13. lsugano
    • 2 years ago
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    OMG i think i got it!!

  14. hartnn
    • 2 years ago
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    i am glad!

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

  16. lsugano
    • 2 years ago
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    but 5 = √5 . √5

  17. hartnn
    • 2 years ago
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    es, you can do that way also!

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

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

  20. hartnn
    • 2 years ago
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    no problem at all :) welcome ^_^

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