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## anonymous 5 years ago how do i simplify a radical expression that has a variable in it?

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1. anonymous

$\sqrt[3]{x^7}$

2. amistre64

make it a rational exponent :)

3. anonymous

$x^{7/3}$

4. amistre64

x^(7/3) = x^(6/3 + 1/3) x^2 cbrt(x)

5. anonymous

it needs to be simplified not solved

6. amistre64

that is simplified; in order to 'solve' we would have said x = some number

7. amistre64

to simplify just means to write it in another way

8. amistre64

cbrt(x^7) = x^2 cbrt(x)

9. anonymous

ok thanks but all the answers have either a 3 and an x or a 2 and a 3 and an x

10. amistre64

maybe it more accurate to write it like this: cbrt(x^7) <=> x^2 cbrt(x) :)

11. amistre64

$\sqrt[3]{x^7} <=> x^2 \sqrt[3]{x}$

12. anonymous

thank you so much

13. amistre64

yw :)

14. anonymous

$\frac4{9-\sqrt6}$

15. anonymous

rationalize the denimonator

16. amistre64

you gotta multiply by the conjugate; which is just cahngeing that - into a +

17. amistre64

4 (9+sqrt(6)) 4(9+sqrt(6)) ----------- = ----------- 81 -6 75

18. amistre64

multiply top AND bottom by the conjugate ;)

19. anonymous

thx

20. amistre64

yw :) if you post a new question in the question box, more people will get a chance to help and you wont run the risk of me not seeing it in this post :)

21. anonymous

$\log_{5}75-\log_{5}3$

22. anonymous

write the expression as a single logarithm whose coefficient is 1?

23. amistre64

log(a) - log(b) = log(a/b) so, log5(75) - log(3) = log5(75/3) = log5(25)

24. anonymous

$\sqrt{9x+22}=x$

25. amistre64

^2 both sides to get: 9x +22 = x^2 0 = x^2 -9x +22 0 = (x-11)(x+2) x = 11 and -2 ; but we gotta dbl check because this way can have fake results: sqrt(9(11)+22) ?= 11 sqrt(99+22) ?= 11 sqrt(121) ?= 11 11 = 11 ; that ones good -------------------------------- sqrt(9(-2) +22) = -2 .... aint no way that one works lol x = 11 is the answer

26. anonymous

u r a math god!!

27. amistre64

more of a math demigod lol

28. anonymous

lol

29. amistre64

my indian name is "runs with scissors" ....

30. anonymous

$\log_{9}25$

31. anonymous

calculator keeps giving me the wrong answer

32. amistre64

change of base it.... is my guess

33. amistre64

ln(25) ----- = answer ln(9)

34. amistre64

1.464.... maybe?

35. anonymous

thanks that worked

36. amistre64

it should :)

37. amistre64

spose we have 9^x = 25 log(9^x) = log(25) x log(9) = log(25) x = log(25)/log(9) x = log9(25) its all good

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