A2 maths Proof by Contradiction

Hi, anyone able to help me with this proof question?

Prove by contradiction that square root k, where k is a prime number, is an irrational number.
You may use without proof the fact that any positive integer may be written uniquely as a product of its prime factors.

Thanks :biggrin:

(edited 7 months ago)

Reply 1

DFranklin

Original post by tealpencil

Hi, anyone able to help me with this proof question?

Prove by contradiction that square root k, where k is a prime number, is an irrational number.

Thanks :biggrin:

What have you done so far?

You should basically be able to copy the proof that sqrt(2) is irrational (which I assume you know).

Reply 2

tealpencil

Original post by DFranklin

What have you done so far?

You should basically be able to copy the proof that sqrt(2) is irrational (which I assume you know).

let sqrt k = a/b where a and b are integers and b does not = 0
k= a^2 / b^2
kb^2=a^2

Reply 3

mqb2766

Original post by tealpencil

let sqrt k = a/b where a and b are integers and b does not = 0
k= a^2 / b^2
kb^2=a^2

So what can you say about the prime factors of a^2 and b^2 and what happens when you multiply b^2 by the prime number/factor k?

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A2 maths Proof by Contradiction

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