Question

Show that 2/5underroot 3 is irrational number.

Answer 1

Answer:

Step-by-step explanation:

let root 3an rational number

therefore,root3 = p/q (where pand q are integers and q not=0)

(squaring on both the sides )

we get

3=p^2/q^2

3q^2=p^2

therefore ,

3 divides p^2

so,3divides p

let us take that p=3c

where c is co prime

so, 3q^2=9c^2

q^2 =3c^2

so

3 divides c^2

3 divides c

This contradiction had arisen due to our false assumption

so root 3 is rational is wrong

so root 3 is irrational