Question

show that√3 is not a ratioal number

Answer 1

let's root √3 be a rational number.

now √3=a/b (because a rational number can be written in the form of a /b.)

now,

√3=a/b

squaring both sides

3 = a^2/b^2

a^2=3b^2

now 3 is a factor of a square

also 3 is a factor of a.

let's a equal to 3 c.

then equation one can be written as-

3b^2=(3c)^2

3 is a factor of b square

also 3 is a factor of B.

no we see that 3 is a factor of a and b both so it contradicts our supposition that root 3 is rational.

so root 3 is a irrational number...