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

1. hartnn

because $$\huge \frac{\sqrt 5}{5}=\frac{\sqrt 5}{\sqrt5.\sqrt 5}=\frac{1}{\sqrt 5}$$

2. lsugano

i still dont get it..><

3. hartnn

$$\huge \frac{2\sqrt 5}{5}=\frac{2\sqrt 5}{\sqrt5.\sqrt 5}=\frac{2}{\sqrt 5}$$ which step ?

(2√5)/5 can also be written as $\frac{ 2 }{ \sqrt{5} }$

5. hartnn

reciprocal means inversing the ratio, a/b becomes b/a

6. lsugano

why is the denominator √5 multiply by √5

7. hartnn

any number can be expressed as $$a=\sqrt a.\sqrt a$$

8. hartnn

$$x^m.x^n=x^{m+n} \\so, \huge \sqrt 5.\sqrt 5= 5^{1/2}.5^{1/2}=5^{1/2+1/2}=5^1$$

9. hartnn

doubts ?

10. lsugano

wait basically....√5 and 5 is the same?

11. hartnn

no.... 5 and $$\sqrt 5.\sqrt 5$$ are same.

12. lsugano

but why do we have to multply by √5??

13. lsugano

OMG i think i got it!!

14. hartnn

15. lsugano

so first, the reciprocal of (2√5)/5 is 5/2√5

16. lsugano

but 5 = √5 . √5

17. hartnn

es, you can do that way also!

18. lsugano

and √5 crosses out which equals. √5 / 2!!

19. lsugano

thank you soooo much!!!! im sorry if i put some streess on you!! i am really bad at math ><

20. hartnn

no problem at all :) welcome ^_^