Question

26. Prove 5 - √2 is irrational, given that √2 is irrational.​

Answer 1

Answer:

Let us assume the given number be rational and we will write the given number in p/q form

⇒5−3=p/q

⇒3=5q−p/q

We observe that LHS is irrational and RHS is rational, which is not possible. 

This is contradiction. 

Hence our assumption that given number is rational is false 

⇒5−3  is irrational

Answer 2

Answer:

Given that √2 is irrational

Let us assume that 5 - √2 is rational

Therefore, 5 - √2 =  a/b , where a and b are co prime

√2= 5-a/b

LHS is irrational, RHS is rational

This contradicts the fact that √2 is irrational

This contradiction has arisen because our assumption is wrong

Thus 5 - √2 is irrational

Hope this helps :)

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