Question

√m is an irrational number then m must be​

Answer 1

Step-by-step explanation:

let us assume on the contrary that √m is rational no. thus can be written in the form of 0

p/q

i.e, p/q=m

squaring both sides we have

p²/q²=m²

p²=q²m²(according to theorem p² divides m²)......(1)

now let c be multiple of m

m=qc

squaring c²=m²

thus after putting eq(1) in c²=m² we found that q divides m.....(2)

thus from eq(1&2) m has two factors other than one hence our assumption was wrong√m is irrational no.