## anonymous one year ago simplify radical -25

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1. anonymous

@TheSmartOne @JoannaBlackwelder

2. anonymous

|dw:1437498244836:dw|

3. Nnesha

$\huge\rm \sqrt{-25}$ factor out -1 $\huge\rm \sqrt{-25} = \sqrt{-1} \times \sqrt{25}$ and combine like terms 't the denominator

4. anonymous

What does $\sqrt{-25}$ simplify into? Hint: 25 is a perfect square.

5. anonymous

5

6. Nnesha

and $\sqrt{-1} = ???$

7. anonymous

idek

8. Nnesha

$i = \sqrt{-1}$ $i^2 = -1$

9. anonymous

so now what

10. anonymous

√-1=i

11. Nnesha

|dw:1437498682455:dw| now combine like terms (5-2i) +( 1-3i)

12. anonymous

5i

13. Nnesha

so you can replace sqrt of -1 by i

14. anonymous

so what would the answer be?

15. anonymous

√25 simplifies to 5 and √-1 simplifies to i and they multiply to make 5i

16. anonymous

got that?

17. Nnesha

that's what you should find ot

18. anonymous

|dw:1437498844568:dw|

19. anonymous

i got 5+20i/17

20. anonymous

its 5i

21. anonymous

T^T

22. Nnesha

and how did you get that ?

23. anonymous

√25 simplifies to 5 and √-1 simplifies to i and they multiply to make 5i

24. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @LorenaHue43 i got 5+20i/17 $$\color{blue}{\text{End of Quote}}$$ $$\color{blue}{\text{Originally Posted by}}$$ @Nnesha and how did you get that ? $$\color{blue}{\text{End of Quote}}$$

25. anonymous

*sighs* I jusy guessed bc i have no idea what to do

26. anonymous

I got 5i/(6-5i)

27. Nnesha

$\huge\rm (5-2i)+(6-3i)$ combine like terms

28. anonymous

no it is (1-3i)

29. Nnesha

alright now multiply denominator and numerator by the conjugate of (6-5i)

30. Nnesha

$\huge\rm (5-2i)+(1-3i)$ sorry abt that

31. anonymous

30i-25i^2

32. Nnesha

yep numerator is 30i-25i^2 so i^2 = -1 replace i^2 by -1

33. Nnesha

and what about the denominator ?

34. Nnesha

and btw what's the conjugate of 6-5i ?

35. anonymous

36-60i-25i2

36. anonymous

6+5i is the conjugate

37. Nnesha

i have no idea how u got that ?

38. Nnesha

yes right $\huge\rm \frac{ 5i(6+5i) }{ 6-5i(6+5i) }$ 5i times 5i = ?

39. anonymous

25i2

40. anonymous

61

41. Nnesha

yes right so $\huge\rm \frac{ 30i + 25i^2 }{ 61 }$

42. Nnesha

replace i^2 by -1 and done!

43. anonymous

soo -25+30i/61

44. Nnesha

remember $i =\sqrt{-1}$ i^2 = -1

45. Nnesha

yes right

46. anonymous

47. Nnesha

who gave u the answer ?

48. anonymous

I solved it..

49. Nnesha

alright.

50. anonymous

|dw:1437499746192:dw|

51. anonymous

simplify that please. I got 2/6-5/5 (idek where the radical sign is)

52. Nnesha

what are factors of 24 ,45 and 20 ?

53. anonymous

24=4,6 45=9,5 20=4,5

54. Nnesha

yes right |dw:1437499992200:dw| 4,9 ,4 are perfect square root

55. anonymous

So then I was right?

56. Nnesha

multiply |dw:1437500190222:dw| multiply those numbers and there are common sqrt{5} so you can combine last two terms

57. Nnesha

what did you get ? sorry i was afk

58. anonymous

|dw:1437500682025:dw|

59. Nnesha

did you use calculator ?

60. anonymous

no,

61. Nnesha

alright that's right but next time DON'T forget to post ur work thanks

62. anonymous

:) Thank you!

63. anonymous

I have one more to ask. I really don't understand

64. Nnesha

make a new post

65. anonymous

will do

66. mathstudent55

$$\dfrac{\sqrt {-25}} {(5 - 2i) + (1 - 3i)}$$ $$= \dfrac{\sqrt {-1} \sqrt{25}} {5 - 2i + 1 - 3i}$$ $$= \dfrac{i \times 5} {6 - 5i}$$ $$= \dfrac{5i} {6 - 5i} \times \dfrac{6 + 5i}{6 + 5i}$$ $$= \dfrac{5i (6 + 5i)} {(6 - 5i)(6 + 5i)}$$ $$=\dfrac{30i + 25i^2}{6^2 - (5i)^2}$$ $$= \dfrac{30i + 25(-1)}{36 - 25(-1)}$$ $$=\dfrac{-25 + 30i}{36 + 25}$$ $$=\dfrac{-25 + 30i}{61}$$ $$= -\dfrac{25}{61} + \dfrac{30}{61}i$$

67. mathstudent55

|dw:1437501142771:dw|