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Answer 1

Prove that √3 is an irrational number?

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1 ANSWER



Sandeep Sharma, studied at Indian Institute of Information Technology, Allahabad

Answered Feb 27, 2017

We can provide a contradictional proof for it..

Firstly let us assume

Assumption:let √3 be a rational ….then as every rational can be represented in the form p/q where q≠0

Let √3=p/q where p,q have no common factor.

Now squaring on both sides we get 3=p^2/q^2

i.e 3*q^2=p^2

Which means 3 divides p^2 which implies 3 divides p

Hence we can write p=3*k

This gives 3*q^2=9*k^2

q^2=3*k^2

Which means 3 divides q^2 which implies 3 divides q.

3 divides p and q which means 3 is common factor for p and q.

And this is contradiction for our assumption that p and q have no common factor…

Hence we can say our assumption that √3 is rational is wrong…

And therefore √3 is an irrational…

Answer 2

lthis is your required answer