## Anguyennn one year ago how to simplify 2√4-√9?

1. jim_thompson5910

What is the square root of 4 equal to?

2. Anguyennn

2

3. jim_thompson5910

correct What is the square root of 9 equal to?

4. Anguyennn

3

5. Anguyennn

and you multiply 2x2 and minus 3? correct?

6. jim_thompson5910

so you really have 2*2-3 evaluate that to get ??

7. jim_thompson5910

correct

8. Anguyennn

oh ok!! thank you but what about when its √2?

9. jim_thompson5910

taking the square root of 2 doesn't give a whole number like the square root of 4 does

10. Anguyennn

like 3√2-5√2-2√2

11. jim_thompson5910

I don't see a square root of 2 in your problem though

12. jim_thompson5910

Oh I see now

13. jim_thompson5910

replace every copy of "square root of 2" with x so you'll have 3x-5x-2x simplify that to get ???

14. Anguyennn

-4x

15. Anguyennn

but how come you replaced it with an x?

16. jim_thompson5910

well you don't need to, but you can think of it like that basically you're combining like terms. In this case, all 3 terms are like terms because they have a root 2 in them

17. Anguyennn

yes

18. jim_thompson5910

3x-5x-2x = -4x so you now replace the x with square root of 2 so the final answer is $$\Large -4\sqrt{2}$$

19. Anguyennn

i am still confused because for other questions it would have different numbers and i don't know how to do them

20. jim_thompson5910

like what for example?

21. Anguyennn

√18+√50-√8

22. jim_thompson5910

have you tried to simplify each root?

23. Anguyennn

dividing them all by 2?

24. jim_thompson5910

think of all of the factors of 18 which factors are perfect squares?

25. Anguyennn

I am not sure

26. Anguyennn

sorry

27. jim_thompson5910

factors of 18 1,2,3,6,9,18

28. Anguyennn

ok

29. jim_thompson5910

which factor is a perfect square?

30. Anguyennn

9

31. jim_thompson5910

so we can say this $\Large \sqrt{18} = \sqrt{9*2}$ $\Large \sqrt{18} = \sqrt{9}*\sqrt{2}$ $\Large \sqrt{18} = 3*\sqrt{2}$

32. jim_thompson5910

I factored 18 into 9*2 then I used the rule $\Large \sqrt{x*y} = \sqrt{x}*\sqrt{y}$

33. Anguyennn

yes

34. jim_thompson5910

now let's do 50 what are the factors of 50?

35. Anguyennn

1, 2, 5, 10, 25

36. Anguyennn

and it would be 25 that is the perfect square

37. jim_thompson5910

yes so 50 = 25*2

38. jim_thompson5910

what would $$\Large \sqrt{50}$$ simplify to?

39. Anguyennn

√25x2

40. jim_thompson5910

then break it up using the rule I posted

41. Anguyennn

√50= √25x2 =√25x √2 5√2

42. jim_thompson5910

good

43. jim_thompson5910

now onto 8 the factors of 8 are ???

44. Anguyennn

1,2,4,8

45. jim_thompson5910

which is a perfect square?

46. Anguyennn

√4

47. jim_thompson5910

so we can say 8 = 4*2

48. jim_thompson5910

then use that rule

49. Anguyennn

√8= √4x2 =√4x√2 2√2

50. jim_thompson5910

so, $\Large \sqrt{18}+\sqrt{50}-\sqrt{8}$ is the same as $\Large 3\sqrt{2}+5\sqrt{2}-2\sqrt{2}$

51. jim_thompson5910

we can replace all the square root of 2 terms with x $\Large 3\color{red}{\sqrt{2}}+5\color{red}{\sqrt{2}}-2\color{red}{\sqrt{2}}$ $\Large 3\color{red}{x}+5\color{red}{x}-2\color{red}{x}$

52. Anguyennn

correct

53. Anguyennn

54. jim_thompson5910

not yet

55. Anguyennn

would you do 3+5-2 now?

56. Anguyennn

and get 6√2?

57. jim_thompson5910

58. Anguyennn

oh ok thank you so much!

59. jim_thompson5910

you're welcome