Math Is Fun Forum
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#1 2014-03-27 18:03:29
Surds
Question One:
Arrange the following in descending order and justify your answer:
2^(1/3) , 3^(1/6), 4^(1/9)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#2 2014-03-27 20:39:03
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Surds
hi Agnishom,
I'm assuming this has to be done without using a calculator.
As 4 = 2^2 you can re-write 4^(1/9) as a power of 2, and hence decide between them.
To compare the power of 2 with the power of 3, you could raise both to the power 6, and compare those answers.
[ If a^6 > b^6 with a and b both > 1, then a > b ]
If that doesn't determine the order of all three, you may need to check the power of 4 against the power of 3 in a similar manner.
Bob
Last edited by Bob (2014-03-27 20:41:28)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2014-03-27 20:40:41
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
Hi;
By raising both of them to the 6th power you can see that
By raising both of them to the 18th power you can see that
So we have
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#4 2014-03-28 00:03:31
Re: Surds
Thanks guys. I'll post Question Two once I am back from the store.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#5 2014-03-28 00:11:14
Re: Surds
Simplify [
]Last edited by Agnishom (2014-03-28 00:11:50)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#6 2014-03-28 00:25:28
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
Hi;
Multiply top and bottom by:
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2014-03-28 03:29:24
Re: Surds
How do you cope with [
]?'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#8 2014-03-28 03:44:34
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2014-03-28 04:15:10
Re: Surds
How did you do that?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#10 2014-03-28 04:58:36
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
I wanted the form a + √b so I hold a constant and solve for b. Worked the first time!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#11 2014-03-28 05:29:28
Re: Surds
Is this wrong? Are you sure that this is equal to what you have given?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#12 2014-03-28 05:34:00
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
Hi;
Of course it is equal.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#13 2014-03-28 05:38:10
Re: Surds
How?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#14 2014-03-28 05:40:43
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
Say
Hold a constant, a = 1 and solve for b.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#15 2014-03-28 05:46:02
Re: Surds
How did you know that a = 1 without solving it?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#16 2014-03-28 05:48:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
When you hold one constant it means you give it a value and solve for the other. If it does not work you give it the next value.
If this were a real world problem I would only do that as a last resort. But in book, contest or forum problems I use it first!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#17 2014-03-28 05:51:00
Re: Surds
How do you know that it is not working? What if a was equal to 1.452814990123?
I have not got the slightest idea what a real world is
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#18 2014-03-28 05:52:30
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
That is why you fail-Yoda
Remember that quote?
You do not consider the poser of the problem very much.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#19 2014-03-28 05:55:12
Re: Surds
We will talk about the philosophy later.
Will the method you are suggesting always work for all these problems?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#20 2014-03-28 05:59:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
Will the method you are suggesting always work for all these problems?
Oh that is a good one. Spoken like a mathematician but not an experimental one. They want methods that always work. If a method works a million times and fails once they will forget it. We work with methods that work most of the time, not all the time.
How did you do that?
But if you really can not follow what has been done then this will jog your memory. Do you remember this nice formula by anonimnystefy?
You can finish now.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#21 2014-03-29 08:14:24
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Surds
That's the one I would use here. The formula was found by Lagrange, though, not me.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#22 2014-03-29 08:26:53
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
Lagrange, Schmagrange, to me it is anonimnystefy's formula.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#23 2014-03-29 09:15:14
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Surds
Sure, I don't think Lagrange is able to complain.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#24 2014-03-29 09:18:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Surds
He can if he wants to, but it will be to no avail.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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