Question

radical expressions please help me step by step on how to do this problems please

I have to simplify and assume that the variables are real numbers
^3pie27(x+3)^3

Answer 1

\[\sqrt[3]{27 (x+3)^3}\]

Answer 2

does anyone know the radical expression

Answer 3

ok, firstly, do you know what this equals?\[\sqrt[3]{x^3}=?\]

Answer 4

thnaks so much I have been reading this over and over and I am so confused on this week work
I have 3 questions to go to be done with this homework and it has taken me forever

Answer 5

x^6 right

Answer 6

no that would be \((x^3)^2\)

Answer 7

here we are finding the cube root of x cubed

Answer 8

ok now you got me lost

Answer 9

ok - lets start with something simpler, what would this equal?\[\sqrt{x^2}=?\]

Answer 10

so would that be (x^2)

Answer 11

or x(x+1)

Answer 12

ok - it looks like you first need to learn about the various rules for exponents.
I suggest you take a look here: http://www.mathsisfun.com/algebra/exponent-fractional.html

and then come back to this problem.

Answer 13

k I will look thanks

Answer 14

yw :)

Answer 15

so that would mean that it would be (xx)

Answer 16

what would this equal?\[\sqrt{x^2}=?\]

Answer 17

(xx)

Answer 18

no - let me try with actual numbers.
what does this equal?\[\sqrt{4}=?\]

Answer 19

2

Answer 20

correct, and what about this?\[2^2=?\]

Answer 21

4

Answer 22

good, so therefore what will this equal?\[\sqrt{2^2}=?\]

Answer 23

would it be 2 since 2X2 is 4 but the SR would be 2

Answer 24

correct, so now use that knowledge to work this out:\[\sqrt{x^2}=?\]

Answer 25

x

Answer 26

correct. now similarly:\[\sqrt[3]{x^3}=x\]because the "cube root" of x "cubed" just gets you back at x. agreed?

Answer 27

yes agree so then the problem would look like this \[\sqrt[3]{27+x}\] right

Answer 28

no - we are not ready to tackle that yet.

Answer 29

oh k no wonder I get lost I want to finish to fast

Answer 30

in your equation you have:\[\sqrt[3]{27 (x+3)^3}\]can you think of some number that, when it is cubed, will give you 27?

Answer 31

would that be like 9*3

Answer 32

another way of phrasing that would be:\[\sqrt[3]{27}=?\]it has to equal ONE number

Answer 33

I believe that is the only number that goes into 27

Answer 34

so then 9

Answer 35

\[9\times9\times9\ne27\]

Answer 36

no that would be 3 3*3*3

Answer 37

correct, so we can rewrite your expression as:\[\sqrt[3]{27 (x+3)^3}=\sqrt[3]{3^3 (x+3)^3}\]correct?

Answer 38

yes correct

Answer 39

now next thing to notice is that:\[a^3b^3=(ab)^3\]therefore:\[3^3(x+3)^3=(3(x+3))^3\]

Answer 40

so then would mulitply the 3 timesx and the 9?

Answer 41

no no no the 3*x and 3*3

Answer 42

no - first do you agree with that last step?

Answer 43

would it be 3(x+x+3) because you have 3^3

Answer 44

I will assume you agree and proceed to the next step.
we now have:\[\sqrt[3]{27 (x+3)^3}=\sqrt[3]{3^3 (x+3)^3}=\sqrt[3]{(3(x+3))^3}\]agreed?

Answer 45

yes

Answer 46

you make it look so easy

Answer 47

:)

now let us substitute:\[y=3(x+3)\]then we end up with:\[\sqrt[3]{27 (x+3)^3}=\sqrt[3]{3^3 (x+3)^3}=\sqrt[3]{(3(x+3))^3}\]\[=\sqrt[3]{y^3}\]agreed?

Answer 48

yes

Answer 49

and by now you should know what:\[\sqrt[3]{y^3}=?\]

Answer 50

y

Answer 51

perfect!

Answer 52

so final answer is:\[\sqrt[3]{27 (x+3)^3}=\sqrt[3]{3^3 (x+3)^3}=\sqrt[3]{(3(x+3))^3}=3(x+3)\]

Answer 53

since we said:\[y=3(x+3)\]

Answer 54

wow see you did make it look easy and understandable thanks so much, can you help me with the other 2 that I have

Answer 55

<--- just post each question separately in the list on the left

that way, others can also help you out - there are lots of very good helpers on this site. I may be busy with some moderator duties but I will keep an eye out for your problems.

Answer 56

k thanks again

Answer 57

yw :)