Question

prove that root 3 is an irrational number.
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Answer 1

HOLA!!!

Let us assume √3 as rational.

Therefore, √3=p/q

( √3)q=p

We can see that LHS is irrational whereas RHS is rational.

So, our preassumption is contradicted.

So, √3 is irrational.

HOPE IT HELPS UHH #CHEERS

Answer 2

Assume root 3 is rational.It can be written as root3=p/q Where q is not equal to 0 and p and q are integers without common factor.

On squaring,

3=p^2/q^2

=>3q^2=p^2

therefore,3 divides p.

p=3k for some integer k.

p^2=9k^2 => 3q^2=9k^2 => q^2=3k^2

3 divides q^2 =>3 divides q.

Here p and q has common factor 3.therefore by method of contradiction,root 3 is irrational.