## anonymous 5 years ago What do I with this?

1. anonymous

$\sqrt{1/3}$

2. anonymous

What do I do with this?

3. amistre64

its fine the way it is; or we can move things around to make it "look" different but still have the same value..

4. anonymous

i want to simplify it but it's already done

5. amistre64

most textbooks will want you to make it in the form: sqrt(3)/3

6. anonymous

$\sqrt{1/3}$ $\times$ $\sqrt{3/3}$ = $\sqrt{3}$/3

7. amistre64

that radical sign can be split so that it is over each number individually like this: sqrt(1) ------ sqrt(3)

8. anonymous

amistre is right...

9. amistre64

sqrt(1) = 1 ------ sqrt(3) = sqrt(3) now most textbooxs HATE to have a radical in the bottom of a fraction so they work on it some more..

10. amistre64

we multiply this fraction by a convient form of (1); because anything times (1) equals itself. Lets use sqrt(3)/sqrt(3) 1 sqrt(3) sqrt(3) ------ (x) ------ (=) -------- sqrt(3) sqrt(3) 3

11. anonymous

heres the problem $2\sqrt{3}+\sqrt{27}-\sqrt{1/3}$ so I simplified it to 2*1.7+5.2-1.7

12. amistre64

ahhhh, then we need all like "radicals" to act like variables: lets change sqrt(27) to look into something that has a sqrt(3) attached to it: do you know how?

13. anonymous

no

14. amistre64

lets see if we can find some numbers that will help us out with that "27" We should know by now that 3 times 9 = 27: 3(9) = 27 also: 3*3*3 = 27 Do you know how to use this knowledge to your advantage?

15. anonymous

the solution is: 2 sqrt 3 + 3 sqrt 3 - sqrt 3/3 time it to 3 =6 sqrt 3 + 9 sqrt 3 - sqrt 3 =14 sqrt 3 thats the answer

16. amistre64

tian: very good :)

17. amistre64

JAPAN: what can we do to: sqrt(3*3*3) to make it look like ___ sqrt(3)? Do you know?

18. anonymous

@amistre thanks but Ur answer is more complete...:-)

19. anonymous

so $3\sqrt{3}$?

20. amistre64

Yes, that is correct. But it is important that you understand HOW you got it. Which if you already know, then great :)

21. anonymous

three 3's multiplied together equal 27 which is how we simplify it

22. amistre64

yes, and what alloed us to pull that "3" out from under the radical? Do you know?

23. amistre64

**allowed

24. amistre64

3*3 = 9 means: 3^2 = 9 we also know that the sqrt(9) = 3 if we put these facts together, we notice a rule or pattern: sqrt(9) = sqrt(3^2) = 3 What allowe us to turn sqrt(3*3*3) into 3sqrt(3) is this "rule" sqrt(3^2 3) = sqrt(3^2) sqrt(3) = 3sqrt(3) Does that make sense?

25. anonymous

yes

26. amistre64

Once you know that, the rest is pretty simple. So your equation becomes: 2 sqrt(3) + 3 sqrt(3) - (1/3) sqrt(3) We can add all these together now and treat that "sqrt(3)" as tho it was a normal variable like "x" or "y". Does that make sense?

27. anonymous

yes thank you

28. amistre64

youre welcome :)