## anonymous 4 years ago can someone help me understand on how to simplify radicals?

1. saifoo.khan

Where are u stuck? do u have any examples?

2. anonymous

how would I simplify 16/81 all under a square root simble?|dw:1327798829785:dw|

3. saifoo.khan

$\sqrt{\frac{16}{81}}$That right?

4. anonymous

yea!!!

5. saifoo.khan

That can we written as, $\frac{\sqrt{16}}{\sqrt{81}}$

6. saifoo.khan

Can you solve now?

7. anonymous

so then it would be like 4 over 9?

8. anonymous

is that simplified?

9. anonymous

|dw:1327799041137:dw|

10. saifoo.khan

Yes 4/9 is correct. but How u got 4/9 ? u simplified using the square root.. So the cancel will be cancelled now.

11. anonymous

oh that makes sense, thank you:) would you be able to help me out with a few more problems?

12. saifoo.khan

$\sqrt{\frac{16}{81}} \to \frac{\sqrt{16}}{\sqrt{81}} \to \frac 49$

13. saifoo.khan

Welcome. How many do u have? i will help u as much as i can.

14. saifoo.khan

i dont have much time though.

15. anonymous

ok, then ill ask you the ones that are more difficult than others

16. saifoo.khan

Feel free to do so.

17. anonymous

how would i simplify |dw:1327799236709:dw|

18. anonymous

and i also am wondering how I would solve$2\sqrt{3}\div3\sqrt{2}$

19. saifoo.khan

$\sqrt{75} \text{ can be written as,} \sqrt{ 25 \times 3} \to 5 \sqrt3$

20. anonymous

ok i got that one thanks:)

21. saifoo.khan

So now u cann those.

22. saifoo.khan

For the second one, That is simplified, but indirectly.

23. anonymous

one more question after the last one i posted is How do i simplify questions that have like 10 over square root 5|dw:1327799591814:dw|

24. saifoo.khan

$\frac{10}{\sqrt5} \times \frac{\sqrt5}{\sqrt5}$

25. anonymous

so for the one thats simplified i would just write simplfyied?

26. saifoo.khan

Idk.. have you guys studied rationalizing?

27. anonymous

um... i don't know

28. saifoo.khan

$\frac{2\sqrt3}{3 \sqrt 2}\times \frac{3 \sqrt2}{3 \sqrt2}$Now u may solve this.

29. anonymous

i cross multiply?

30. saifoo.khan

Nope, simply multiply. You ONLY cross multiply when there's a "=" sign in between.

31. anonymous

ah, i see

32. anonymous

Just a nice couple of things about radicals. If a and b are numbers then $\sqrt{ab} = \sqrt{a}\sqrt{b}$ $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ and if n and m are any numbers, then $n\sqrt{a} + m\sqrt{a} = (n+m)\sqrt{a}$

33. anonymous

should add $b \neq 0$ for that second one..

34. anonymous

can you help me with a problem?

35. anonymous

what was the second one?

36. anonymous

the second one is the fraction, one must never divide by zero. Also a and b are obviously nonnegative (unless it's an odd radical)

37. anonymous

um can you help me with a few more questions?

38. anonymous

? what's the problem?

39. anonymous

how would i simplify |dw:1327800649423:dw|

40. saifoo.khan

Rationalize it, $\frac{7}{2 \sqrt2} \times \frac{2 \sqrt2}{2 \sqrt2}$

41. anonymous

why do you multiply it?

42. saifoo.khan

Whenever u have a sqrt in bottom part. we always do it that way to simplify it. The method is known as rationalizing. in which we multiply and divide the fraction by the denomiator.

43. anonymous

ok, so im stupid, so can you help me multiply that?

44. saifoo.khan
45. anonymous

46. saifoo.khan

(:

47. saifoo.khan

Bye, c ya.

48. anonymous

c ya too

49. anonymous

on that last one it was sufficient to just multiply by $\frac{\sqrt{2}}{\sqrt{2}}$

50. anonymous

which one was that?

51. anonymous

is|dw:1327802012909:dw|

52. anonymous

Ok, suppose you have a fraction like this $\frac{7}{2\sqrt{2}}.$ You want to rationalise the denominator, which means - make the number on the bottom into something without roots. Now multiplying this fraction by 1 will not change it. Notice that $1 = \frac{\sqrt{2}}{\sqrt{2}}$ and this is true for anything: something divided by itself equals 1. Therefore $\frac{7}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{7\sqrt{2}}{2(\sqrt{2})^2}$ Now the squared removes the square root and you are just left with 2: $(\sqrt{2})^2 = 2$ So we get in the end: $\frac{7\sqrt{2}}{4}$ and this is equal to what you started with, and the change we have made is we have rationalised the denominator.

53. anonymous

thank you

54. anonymous

That's wrong by the way, $\sqrt{1} + \sqrt{1} = 2\sqrt{1}$ because there is two of them! and we know that $\sqrt{1} = 1$ so $\sqrt{1} + \sqrt{1} = 2\sqrt{1} = 2$

55. anonymous

and so the square root of 1 +the square root of 1 is 2?

56. anonymous

yes, since the square root of 1 is 1, so it reduces to 1+1!

57. anonymous

ah, thank you:) I have now finished my math assignment. You have helped me so much, instead of just giving me the answers you helped me understand it

58. anonymous

no problem! Hope it's been a help