Question

1. Prove that √5 is irrational.(maths​

Answer 1

Answer:

first we have to assume that√2 is irrational which is contradiction and slowly we have to do the process of this problem

Answer 2

Step-by-step explanation:

Let assume to the countrary , that √5 is rational

Now  

Let root5a/b  where a and b are co prime  

Squaring on both sides  

5 = a^2 / b^2

5b^2 = a^2

This shows that a^2 is divisible by 5

It also shows that a is also divisible by 5

Let a = 5m for some integer m

Put a = 5m in 5b^2 = a^2

5b^2 = (5m)^2

5b^2 = 25m^2

b^2 = 5m^2

Hence

b^2 is divisible by 5  

So b is also divisible by 5

From above we can say that 5 is a common factor for both a and b

But this contradicts our assumption that a and b are co prime

Hence √5 is an irrational number .

Hence  Proved

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