Question

Prove that root 5 is a irrational

Answer 1

Let us assume that√5 =a/b where a and b are comprime numbers and b not equal to 0.therefore √5 is rational

√5=a/b

Squaring both sides

5=a2/b2

5b2=a2.......(1)

(If 5 divides a2 then 5 divides a)

Let a/5=c

a=5c.......(2)

(2)in(1)

5b2=(5c)2

b2=5c2

( If 5 divides b2 then 5 divide b)

Therefore a and b have common factor 5.

So it contradicts our assumption that √5 is rational. Therefore our assumption is wrong.

Hence √5 is irrational.

Proved...

Hope it helps..

Similarly u can prove √3,√7,etc irrational