Question

13. Show that 7 - 4√5 is an irrational number, where √5 is given to be an irrational number.
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Answer 1

Given:- root5 is irrational number.

To prove:- 7-4root5 is irrational number.

Proof:-

let,

7-4root5 is a rational number,

such that,

=>7-4 root 5=a/b

=>-4root5 =a-7/b

=>root5 =a-7/-4b

As it given that root 5 is irrational number so,

a-7/-4b is also irrational number.

therefore our assumption is wrong.

Hence,7-4root5 is irrational number.

(hence proved)