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## anonymous 4 years ago Square root of 8y^5 X the square root of 40y^2

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1. anonymous

to multiply variables with exponents, you add the exponents together

2. anonymous

oh there's a square root

3. anonymous

$8y^5(\sqrt{40y^2})?$

4. anonymous

you can pull a y out of the square root because $\sqrt{y^2}=y$

5. anonymous

you can also pull a 2 out of the square root because of $\sqrt{2^2*10}$

6. anonymous

$\sqrt{8y^{5}} * \sqrt{40y ^{2}}$no its

7. anonymous

ok

8. anonymous

you can put it all under one square root

9. anonymous

such as this $\sqrt{(8y^5)(40y^2)}$

10. anonymous

then i got $\sqrt{320y ^{7}}$

11. anonymous

yep

12. anonymous

now you have to pull numbers and variables out

13. anonymous

as a hint, 64*5=320

14. anonymous

then change 320 to $8\sqrt{5}$ then $8\sqrt{5y ^{7}}$ but i dont know what to do next

15. anonymous

yes $8\sqrt{y^7}$

16. anonymous

im sorry $8\sqrt{5y^7}$

17. anonymous

now you can factor y

18. anonymous

if there was a y^2 in there, you would just take out the y, correct?

19. anonymous

into 4 and 3

20. anonymous

yeah that too

21. anonymous

so what if you factored $y^7$ as $y^6y$

22. anonymous

i thought i have to factor it into a perfect square?

23. anonymous

$y^6=(y^3)^2$, if you remember the rules of exponents

24. anonymous

so can you pull y^6 out now?

25. anonymous

$8\sqrt{5y ^{6}}y$

26. anonymous

yes, but now $y^6=(y^3)^2$, which is a perfect square

27. anonymous

$8\sqrt{5y^6y}$

28. anonymous

$=8\sqrt{5(y^3)^2y}$

29. anonymous

if i said y^3=x, then you would see an x^2 inside of the square root

30. anonymous

and you'd pull the x out of $\sqrt{x^2}$

31. anonymous

see what i'm talking about?

32. anonymous

but then i have 8y^3 square root of 5y^3y

33. anonymous

nope, you'd pull the y^3 out of the root, leaving you with only the other y

34. anonymous

$8\sqrt{5(y^3)^2y} = 8y^3\sqrt{5y} =$

35. anonymous

forget that last = sign, that is it. it's done now

36. anonymous

there's no way to make perfect squares from factors of 5 or y

37. anonymous

understand that when you raise a power to a power, you multiply the exponents

38. anonymous

i kind of get it i think..i just have to have more practice because it's still kind of confusing but ill get it

39. anonymous

yeah that's all it takes is practice

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