kswales1
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Hi! Does someone mind helping me with this question? I don't really know where to start

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RDKGames
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(Original post by kswales1)
Hi! Does someone mind helping me with this question? I don't really know where to start

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Begin by assuming that P is irrational and 1/P is rational.

What form can 1/P be written in?
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kswales1
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(Original post by RDKGames)
Begin by assuming that P is irrational and 1/P is rational.

What form can 1/P be written in?
If 1/P is rational then it can be written as a fraction i.e a/b ?
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RDKGames
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(Original post by kswales1)
If 1/P is rational then it can be written as a fraction i.e a/b ?
Yeah so what does mean for P itself? Hence write down the contradiction.
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dextrous63
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(Original post by RDKGames)
Begin by assuming that P is irrational and 1/P is rational.

What form can 1/P be written in?
For (b), are integer multiples of surds irrational or rational?
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username5737602
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(Original post by dextrous63)
For (b), are integer multiples of surds irrational or rational?
If the surd is irrational, any integer multiple of it will be irrational. It makes sense it you think about it. But for b, all you need to do is think of 2 numbers that that multiply to get a square number. For example 2 and 8. 2^1/2 mutpliplied by 8^1/2 equals 16^1/2 equals 4, which is rational
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dextrous63
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(Original post by tej3141)
If the surd is irrational, any integer multiple of it will be irrational. It makes sense it you think about it. But for b, all you need to do is think of 2 numbers that that multiply to get a square number. For example 2 and 8. 2^1/2 mutpliplied by 8^1/2 equals 16^1/2 equals 4, which is rational
Well done tej, you recognised the hint I was giving. After all 8 = 2sqrt(2)
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RDKGames
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(Original post by dextrous63)
For (b), are integer multiples of surds irrational or rational?
Irrational.
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RDKGames
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(Original post by tej3141)
If the surd is irrational, any integer multiple of it will be irrational. It makes sense it you think about it. But for b, all you need to do is think of 2 numbers that that multiply to get a square number. For example 2 and 8. 2^1/2 mutpliplied by 8^1/2 equals 16^1/2 equals 4, which is rational
Maybe simpler to use part (a) then choose a=rt(2) and b=1/rt(2)
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dextrous63
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(Original post by RDKGames)
Irrational.
I know. Was hinting the op. Alas, I quoted you instead of him/her
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