## anonymous one year ago help

1. anonymous

$r^2=\frac{ 9 }{ 2 }$

2. anonymous

$r=\frac{ 3\sqrt2 }{ 2 }$

3. anonymous

How did 9 become,

4. anonymous

$3\sqrt2$

5. Nnesha

got it okay so you have to take square root both sides to cancel out the square

6. Nnesha

$\huge\rm \sqrt{r^2}=\sqrt{\frac{ 9 }{ 2 }}$ square root both sides

7. Nnesha

$\sqrt{r^2} = r$ square root cancels with the square because when you convert square root to exponent you will get $\huge\rm \sqrt{r^2} = r^\frac{ \cancel{2} }{\cancel{ 2} }$ according to this exponent rule $\large\rm \sqrt[n]{x^m} = x^\frac{ m }{ n }$

8. Nnesha

now solve right side $\sqrt{\frac{ 9 }{ 2 }}$ is same as square root of 9 and 2 $\sqrt{\frac{ 9 }{ 2 }}=\frac{ \sqrt{9} }{ \sqrt{2} }$ you can't have the radical sign at the denominator of the fraction so that's why multiply both the denominator and numerator of the fraction by sqrt{2}(denominator)

9. anonymous

ohh right i get it now!

10. Nnesha

(multiply top and bottom of the fraction by the denominator which is sqrt{2}_

11. Nnesha

u sure ? :)

12. anonymous

yes let me show you.

13. Nnesha

okay :)

14. anonymous

$\sqrt{r^2} =\frac{ \sqrt9 }{ \sqrt2 }$

15. anonymous

sec

16. anonymous

$r=\frac{ 3 }{ \sqrt2^\frac{ 1 }{ 2 } }\times \frac{ \sqrt2 }{ \sqrt2\frac{ 1 }{ 2 } }$

17. anonymous

$r=\frac{ 3\sqrt2 }{ 2 }$

18. Nnesha

so why did you write sqr{2} to the 1/2 power ?

19. anonymous

are you testing me, or you don't know why?

20. Nnesha

hahah i'm asking a question :)

21. Nnesha

actually i don't know why did you write square root AND 1/2 power

22. anonymous

i actually don't know how it works..

23. anonymous

but i know it's correct.

24. Nnesha

no $\huge\rm \sqrt{x} = x^\frac{ 1 }{ 2 }$ 1/2 is same as square root of something

25. Nnesha

you can write $\frac{ }{ 2^\frac{ 1 }{ 2 } \times 2^\frac{ 1 }{ 2 }}$ then you don't need to write square root

26. anonymous

hmm

27. anonymous

w8 w8 w8

28. anonymous

i remember who told me this i will link you to the question.

29. Nnesha

don't get it ? it's okay so this is the exponent rule $\sqrt[n]{x^m}=x^\frac{m }{ n}$

30. anonymous

oh wait i think i get it

31. Nnesha

so square root of sqrt{2} is 2^1/2 power $\huge\rm \sqrt{2} = 2^\frac{ 1 }{ 2 }$ when you changed to exponent form then you don't need square root

32. anonymous

oh right!! you are right lol.

33. anonymous

the guy told me the same thing you're telling me now! sorry!!!!

34. Nnesha

ye same thing $\sqrt{3}=3^\frac{ 1 }{ 3 }$

35. Nnesha

it's okay :)

36. anonymous

1/3? you mean 1/2?

37. Nnesha

2 i did type 2 or is it 3 o.O

38. anonymous

its 3 lol.

39. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @Nnesha ye same thing $\sqrt{3}=3^\frac{ 1 }{ 3 }$ $$\color{blue}{\text{End of Quote}}$$ $\huge\rm \sqrt{3}=3^\frac{ 1 }{ 3 }$ ohh i see now yea i meant 2 :)

40. anonymous

lol ok thanks!