## pokemon23 3 years ago Can someone tutor me in multiplying and dividing radicals? Please no nonsense I want to learning

1. Mimi_x3

2. pokemon23

|dw:1326159651743:dw|

3. Mimi_x3

Just multiply. $5*7\sqrt{8*3}$

4. UnkleRhaukus

${1 \over√a} = {1 \over√a} \times {√a \over √a}={√a \over a}$

5. pokemon23

so?

6. Mimi_x3

can't you times it.

7. Mimi_x3

Yes!

8. pokemon23

|dw:1326159934510:dw|

9. Mimi_x3

Correct!

10. Mimi_x3

Want to simplify it further?

11. pokemon23

12. pokemon23

how do you simplify it further?

13. BlingBlong

what times what gives 24, 6*4 so 35(6)^(1/2)*(4)^(1/2) or $35\sqrt{4}\sqrt{6}$

14. pokemon23

can we simplify it further

15. BlingBlong

now you can take the square root of 4 which is 2 therefore you are left with 35(2)(6)^(1/2)

16. BlingBlong

which is just equal to $70\sqrt{6}$

17. pokemon23

so its |dw:1326160227547:dw|

18. pokemon23

how can we simplify it their?

19. BlingBlong

you can't

20. BlingBlong

if you take the square root of 2 you end up with an irrational number which can only be approximated

21. Mimi_x3

Pokemon, you can just use a calculator to check, if you type that in the calculator, it won't equal the same to $5\sqrt{8}*7\sqrt{3}$

22. pokemon23

|dw:1326160630061:dw| to the solution

23. Mimi_x3

$35*2\sqrt{6}$

24. Mimi_x3

since $\sqrt{4} = 2$

25. pokemon23

how? how did you get the solution

26. Mimi_x3

Hmm...where don't you understand? It has been explained thoroughly.

27. BlingBlong

2*2 is = 4, when you take the square of a number it will tell you what two exact numbers can be multiplied together to give you the original number

28. BlingBlong

Radicals are simply the opposite of exponents. If you had just say 3^(3) = (3)(3)(3) = 27 27^(1/3) =3

29. BlingBlong

Thus (4)^(1/2) = 2 because 2*2 = 4

30. BlingBlong

You need to memorize the fundamental rule in radicals that (ab)^(1/2) = $\sqrt{a}\sqrt{b}$

31. BlingBlong

if you wish to simplify radicals further, usually I'm to lazy to do this though :d

32. Mimi_x3

You can simplify it further but you don't need to, it depends on the question.

33. BlingBlong

In your case 35(24)^(1/2) = $35\sqrt{6}\sqrt{4}$

34. pokemon23

thanks for the help

35. BlingBlong

since 35 is being multiplied by the radical when (4)^(1/2) is simplified to 2 you are left with 35(2)(6)^(1/2) if you take the square root of 6 you are going to end up with a very ugly number and in mathematics they usually like you to deal with exact numbers

36. pokemon23

you can reduce to 35|dw:1326161502375:dw|

37. BlingBlong

No problem I hope you have gained a better understanding of radicals, I would recommend look up the fundamental rules of radicals

38. BlingBlong

Once you know all the basic algebraic laws, math becomes a lot easier

39. BlingBlong

the final answer being 70(6)^(1/2) but I will stop posting now :D