anonymous 5 years ago simply. assume all variables represent positive real numbers (sqrt = quare root): 1.) sqrt. 96x^2 y 2.) ^4 sqrt. 16a^4 3.) ^3 sqrt. 64x^4 y^5

1. anonymous

2. anonymous

i dont understand what you are supposed to find out.

3. anonymous

like whats it on? on my exam it just says to simplify

4. anonymous

its 3 different problems

5. anonymous

$\sqrt{96x ^{2}y}=\sqrt{16*6x ^{2}y}=4x \sqrt{6y}$

6. anonymous

$\sqrt[4]{16a ^{4}}=\sqrt[4]{(2a)^{4}} = 2a$

7. anonymous

$\sqrt[3]{64 x ^{4}y ^{5}}=\sqrt[3]{(4xy)^{3}xy ^{2}}=4xy \sqrt[3]{xy ^{2}}$

8. anonymous

THANK YOU SO MUCH !

9. anonymous

can you help me out please with a couple more problems?

10. anonymous

no, I can't do your problems for you. I have shown you how to do these problems. You can do the rest on your own if you apply the same logic. if you have doubts, feel free to ask and I will clarify.

11. anonymous

aw okay , thanks though. but for adding and subtracting them with others would they need the same sqrt inside ?

12. anonymous

give me an example.

13. anonymous

[2 sqrt. 128] + [5 sqrt. 32] + [2 sqrt.200]

14. anonymous

sqrt3 is a number. So if you had 3sqrt 3 +5sqrt3 sqrt 4, you can factor out sqrt3 as if it was a number so it would become sqrt 3 (3+5sqrt4)

15. anonymous

you mean [2 sqrt.200] as sqrt.3 ?

16. anonymous

no , I was giving an example of my own. In your problem you can express sqrt 200 as sqrt 8 sqrt 25. you can express sqrt 32 as sqrt4 sqrt 8. you can express sqrt 128 as sqrt 8 sqrt 16

17. anonymous

how do you know how to express it ?

18. anonymous

you see what is the highest common factor between 200, 32 and 128 and factor it out.

19. anonymous

all 3 have to have the same in common ?

20. anonymous

which would be 8 ?

21. anonymous

yup.

22. anonymous

so answer would be 9 sqrt.8 ?

23. anonymous

the numbers add up to 9

24. anonymous

nope.

25. anonymous

2 + 5 + 2 = 9 ?

26. anonymous

it does

27. anonymous

so if we have the same sqrt. already than just add the numbers which give 9

28. anonymous

yes, but 2 sqrt 200 = 2 sqrt 5 sqrt 8 = 2*5 sqrt 8= 10sqrt8

29. anonymous

sorry 2*sqrt 200 = 2*sqrt 25*sqrt 8 = 2*5*sqrt8 = 10sqrt8

30. anonymous

and simplfying that would give [2 sqrt. 2] ?

31. anonymous

half of each other

32. anonymous

yes, if you want to simply it further, sqrt 8 = 2 sqrt2

33. anonymous

and to simplfy that is 1 ?

34. anonymous

simplify what is 1?