## Anguyennn one year ago How to evaluate √2/3?

1. anonymous

is it $\frac{ \sqrt{2} }{ 3 }$

2. Anguyennn

yes

3. jackthegreatest

just think of it as $\sqrt{2} \times \frac{ 1 }{ 3 }$

4. anonymous

It's an irrational number, it cannot be evaluated, you can only approximate it, $\sqrt{2} \approx 1.4142$ so we have $\frac{\sqrt{2}}{3} \approx \frac{1.414}{3}=0.471333....$

5. Anguyennn

are you sure?

6. anonymous

Usually even upto 3 decimal digits is a good approximation if required

7. Anguyennn

8. Anguyennn

how would you evaluate this?

9. Anguyennn

|dw:1442687878850:dw|

10. anonymous

$\frac{3}{\sqrt{3}}=\frac{\sqrt{3}\sqrt{3}}{\sqrt{3}}=\sqrt{3} \approx 1.732$

11. anonymous

Notice that if you square 1.732, you get $(1.732)^2=2.999824 \neq 3$

12. anonymous

So it is only an approximation

13. Anguyennn

but at the back of my answers it is showing √3 as the answer

14. anonymous

|dw:1442698187908:dw| $\frac{ \sqrt{2} }{ 3 }=\frac{ 1.414 }{ 3 }=0.471 \approx$

15. anonymous

That is the exactl answer, $\sqrt{3}$ is the exact answer $1.732$ is an approximation, if someone asks what is the answer you'd say $\sqrt{3}$ but if you for example need a value, you can use an approximate value

16. Anguyennn

I know that you multiply the denominator by √3 and the numerator as well but how do you get the answer as √3?

17. anonymous

$\frac{3}{\sqrt{3}}=\frac{(\sqrt{3})^2}{\sqrt{3}}=(\sqrt{3})^{2-1}=(\sqrt{3})^{1}=\sqrt{3}$

18. anonymous

you simply cancel a factor of root 3

19. Anguyennn

how did you get (√3)^2?

20. anonymous

3 can be thought of the square of square root of 3, just like how you can write for example 10 as 2 times 5, I've written 3 as root 3 times root 3, or square of root 3 $3=\sqrt{3} \times \sqrt{3}=\sqrt{9}=(\sqrt{3})^2$

21. Anguyennn

ohh ok

22. Anguyennn

oh ok thank you i get it now thank you

23. anonymous

You're welcome

24. Anguyennn

could you help me with one more math problem?

25. anonymous

sure

26. Anguyennn

hello?

27. Anguyennn

r u still there?

28. anonymous

yep I'm here

29. Anguyennn

30. anonymous

Ok, show me your attempt or where you are having a problem

31. Anguyennn

Like I know that you can simplify the 8 by doing √4x2

32. Anguyennn

I just don't know how to do the cubed root

33. anonymous

Ok, let's see Suppose I have |dw:1442689623211:dw| The number outside the radical, which tell which root you have to find, you have to pair up factors that many times inside a root to take them out For example |dw:1442689712453:dw||dw:1442689797599:dw| Now let's suppose a slightly more difficult example |dw:1442689856316:dw|

34. anonymous

another example |dw:1442690185880:dw|

35. Anguyennn

ohh!!!

36. Anguyennn

makes sense, but what about the second part because its a negative 27

37. anonymous

That's slightly tricky! |dw:1442690403700:dw|

38. anonymous

@Anguyennn you there?

39. anonymous

|dw:1442691246474:dw|

40. Anguyennn

hello? i am so sorry the computer was frozen and i did not know how to get back to it until now. i apologize