Question

nswer all the questions:
1. Prove by the method of contradiction that v5 is irrational.
[3]​

Answer 1

the answer is in the picture

Hope It Helps...!!!

Answer 2

step by step : Assume √5 as rational

√5 =a/b [ where a and b are co primes]

a= √5b

squaring on both sides

(a)^2 = ( √5)^2

a^2 =5b^2

here 5 divides a^2

& 5 divides a ------1

a/5 =c cross multiply

5c = a

squaring on both sides

(5c)^2 =(a)^2

25 c^2 =a^2

but a^2 =5b^2

therefore 25c^2 = 5b^2

5c^2 = b^2

5 divides b^2

5 divides b -------2

from 1 and 2 it implies 5 divides both a &b which is a contradiction # to our assumption

therefore √5 is irrational