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**bronxsystem****Member**- Registered: 2013-06-22
- Posts: 63

hey all im trying to learn how to simplify square roots but can only do numbered ones ><

i can do these ones i think

this one i dont understand ><

is that right S: but book says its wrong.

*Last edited by bronxsystem (2014-01-15 10:01:09)*

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**bronxsystem****Member**- Registered: 2013-06-22
- Posts: 63

i think i sort of understand

its because its an unknown right?

like b*b*b = b^3

b^2 * b

and we can write it as

because being unknown doesnt say how many times to do it >< my explanation is terrible but its close right?Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi bronxsystem;

That is one possible simplification.

because being unknown doesnt say how many times to do it

That is not quite correct, the exponent 3 tells you how many times to multiply it. It does not matter whether it is a variable or a constant.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi bronxsystem,

*Edit: I'm not sure if I should have posted this because I don't know the proper method (I've forgotten more than I learnt!), and there's probably a better (or 'book') way to do it. My approach seems to work for these two problems, and so it may help in some way.*

I would look at the first problem like this...

- Find the largest perfect square in 32: ie, 16

- Place its square root (4) in front of the square root sign

- The remaining radicand is 2 (from 32/16 = 2).

The solution for the second problem is identical to that for the first:

- Find the largest perfect square in b³: ie, b²

- Place its square root (b) in front of the square root sign

- The remaining radicand is b (from b³/b² = b³⁻² = b¹ = b)

This next bit is just some additional info that may help with understanding what's going on, but is nothing to do with solving the problems:

The reverse process (ie, to 'unsimplify' the solutions and to revert to the original problems) would be to:

- square the number that is outside the sign (4) to become 16 (or b² for the variable), and

- multiply the result by the radicand to form a new radicand value (ie, 32, or b³).

*Last edited by phrontister (2014-01-16 20:10:24)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bronxsystem****Member**- Registered: 2013-06-22
- Posts: 63

thank you

i sort of understand, enough to do the exercises now but not really comfortable with it.

i will redo the chapter and reread these posts (:

thanks again

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**bronxsystem****Member**- Registered: 2013-06-22
- Posts: 63

thanks for update (:

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Btw, bronxsystem, what is the method you've been taught? I'm curious to see how it compares with my made-up one, and I also might be able to throw some light on it for you.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bronxsystem****Member**- Registered: 2013-06-22
- Posts: 63

i got the hang of it now i can get the answers (:

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Thanks for that, bronxsystem.

Looks like I was close, the main difference being my non-technical wording (which I've now improved in my post) and that I referred to finding the largest perfect square (which I think is correct because simplification is to the lowest form, not an intermediate one...which a lower perfect square - if it exists - would give).

Re the wording of the following:

To summarize, then, a radical can be simplified if the following statements are true:

I would have written that as:

To summarize, then, a radical can be simplified if one or more of the following statements are true:

...for obvious reasons.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bronxsystem****Member**- Registered: 2013-06-22
- Posts: 63

baah sorry guys i know i cant keep posting same thing clogs up thread.

but really hit a wall here.

i got the hang of easy ones but the book throws in different ones without explaining ><

i know i have to some how extract the 9 so that it is same term as the other one.

but cant work out how.

following what phrontister said in post #4

i would square the 2 to make it a 4 then times that by 9 and get 36 is that the first step?

im probably just clicking buttons here but

if above true its written

am i able to write this as

if thats right it makes sense or is it just gorilla math

*Last edited by bronxsystem (2014-01-17 09:47:46)*

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**bronxsystem****Member**- Registered: 2013-06-22
- Posts: 63

EDIT did some reading is this better

*Last edited by bronxsystem (2014-01-17 10:28:09)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

You should be able to do problem now easily.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bronxsystem****Member**- Registered: 2013-06-22
- Posts: 63

yes

really the appreciate help on forum thanks all.

*Last edited by bronxsystem (2014-01-18 06:09:05)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

You're welcome!

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