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Solution


Q.

Prove that 7-35 is an irrational number, given that 5 is an irrational number.

Ans.

Let 7-35 be a rational number such that

7-35=a, where a is a non-zero rational number.

⇒-35=a-7⇒5=a-7-3

Since 7 and 3 are integers and a is a rational number, therefore a-7-3 is a rational number 

⇒5 is a rational number which contradicts the fact that 2 is an irrational number.

Therefore, our assumption is wrong.

Hence 7-35 is an irrational number