Looking for help understanding simplification of this expression with radicals

Hi folks,

I'm trying to teach myself maths at the moment and I have come across a problem that I just cannot get my head around. I have been learning basic algebra and everything has been going well until the final two questions of the test section from the book I have been using (The OXFORD AQA GCSE maths book).

The expression in question is:
(8x22x0.54x3)3

I have tried and tried to get my head around this but I seem to just get myself into ever more of a tangle. I know that I should try and start by seperating the numbers and letters, then working on each side before multiplying it all back together. However, I just cannot work out where to begin here. So far, my best attempt is:

(1): To get the numbers as ( 8 * sqrt(2) ) / 4 which seems to give me 2 * sqrt(2)
(2): I assume I then need to work out the other side, which is sqrt(x^0.5) / x^3 but I am really confused on how to do this.

Sorry if this seems really basic or if I have made stupid mistakes. I am doing my best to get my head around this but numerous attempts, re-readings of my books and google searches have still left me baffled and so I'm hoping someone here can explains things to me step by step.

All the best

James

Naetharu said:

Hi folks,

I'm trying to teach myself maths at the moment and I have come across a problem that I just cannot get my head around. I have been learning basic algebra and everything has been going well until the final two questions of the test section from the book I have been using (The OXFORD AQA GCSE maths book).

The expression in question is:
(8x22x0.54x3)3

I have tried and tried to get my head around this but I seem to just get myself into ever more of a tangle. I know that I should try and start by seperating the numbers and letters, then working on each side before multiplying it all back together. However, I just cannot work out where to begin here. So far, my best attempt is:

(1): To get the numbers as ( 8 * sqrt(2) ) / 4 which seems to give me 2 * sqrt(2)
(2): I assume I then need to work out the other side, which is sqrt(x^0.5) / x^3 but I am really confused on how to do this.

Sorry if this seems really basic or if I have made stupid mistakes. I am doing my best to get my head around this but numerous attempts, re-readings of my books and google searches have still left me baffled and so I'm hoping someone here can explains things to me step by step.

All the best

James

Click to expand...

I'm not sure what your expressions are nor just what the problem is. To take a cut at it, it looks like, from your (1) and (2), that you need to solve for x where
\(\displaystyle \dfrac{\sqrt{x^{0.5}}}{x^3}\, =\, \dfrac{8\, \sqrt{2}}{4}\, =\, 2\, \sqrt{2}\)
If that is correct please confirm. If not, then just what are you trying to solve?

Ishuda said:

I'm not sure what your expressions are nor just what the problem is. To take a cut at it, it looks like, from your (1) and (2), that you need to solve for x where
\(\displaystyle \dfrac{\sqrt{x^{0.5}}}{x^3}\, =\, \dfrac{8\, \sqrt{2}}{4}\, =\, 2\, \sqrt{2}\)
If that is correct please confirm. If not, then just what are you trying to solve?

Click to expand...

Hi, yes you got the right idea there. Sorry about the formatting. I actually had it written out as a proper expression with square root symbols etc. It seems the forum formatting did something horrible to it. I would have addressed it right off but as I am new the post was delayed until a mod checked it.

So to clarify, it is the part you have written out that I am puzzled over. How do I get from the sqrt(x^0.5)/x^3 to the simified version. I am just confused as to how to manipulate the expression. I'm probably overlooking something obvious but I cannot seem to get my head around it.

Naetharu said:

Hi, yes you got the right idea there. Sorry about the formatting. I actually had it written out as a proper expression with square root symbols etc. It seems the forum formatting did something horrible to it. I would have addressed it right off but as I am new the post was delayed until a mod checked it.

So to clarify, it is the part you have written out that I am puzzled over. How do I get from the sqrt(x^0.5)/x^3 to the simified version. I am just confused as to how to manipulate the expression. I'm probably overlooking something obvious but I cannot seem to get my head around it.

Click to expand...

Hints:

\(\displaystyle \displaystyle{\sqrt{x^{\frac{1}{2}}} \ = \ [ x^{\frac{1}{2}}] ^{\frac{1}{2}}}\)

[x^m]ⁿ = x^(m*n)

\(\displaystyle \displaystyle{\dfrac{x^m}{x^n}} \ = \ x^{(m-n)}\)

Denis said:

BUT that's NOT what you should be trying to do.
You should be trying to SOLVE for x.

Click to expand...

Hi Dennis,

Sorry but I don't follow your point. The question I am trying to address, which is one of the ones from my AQA Maths book, asks me to simplify the expression. I'm not sure I follow why this means I should be trying to work out the value of 'x'? Would you be able to explain your point a little more for me?

All the best

James

Naetharu said:

The question I am trying to address, which is one of the ones from my AQA Maths book, asks me to simplify the expression. I'm not sure I follow why this means I should be trying to work out the value of 'x'?

Click to expand...

Sometimes you say that you're needing to simplify an expression, and you seem to imply that the x's are actually multiplication symbols. Other times you say that, yes, you need to solve for the value of x.

Please reply with the full and exact text of the exercise, the complete instructions, and a clear statement of your efforts so far, so we can start to narrow down what it is, exactly, that you're trying to accomplish. If you need to post a scan of the exercise, please make sure that it's large enough to be legible. If you're having trouble with typing math clearly as text, please review formatting advice here. Thank you!

Denis said:

See your answer to Ishuda's post (post#4).

Anyway, simplifying SQRT(x^.5)/x^3 to get 2SQRT(2)
makes no sense...where oh where have the x's gone

MAY WE SEE the problem in its original splendor?

EDIT: whoops, didn't see Stapel's post...
AHA!! There's now 2 of us that you've given a headache to

Click to expand...

I'm really sorry for causing so much confusion. Thank you for having the patience to stick with me and ask helpful questions. Here is the full expression written out again.

Simplify the following: (((8*x^2) * sqrt(2*x^0.5)) / 4*x^3)^3

So that is , Eight times the variable 'x' to the power of two, times the square root of two-times 'x' to the power of one-half, all divided by four-times 'x' to the power of three, and then the whole thing to the power of three.

I'm just confused as to how to approach simplifying this expression as the book that I have been working from has not explained this at all: until now all the questions were a lot more basic but it offered this and another (which I will keep to try and work out on my own once I understand the method). I have tried to work it out but a few days of puzzling has left me stumped. Any insight you could offer me into the method would be very much appreciated.

Thank you again

All the best

James