Question

Prove
that
given
5-root 3 is irrational of it is given that root 3 is irrational ​

Answer 1

Answer:

hence 5-√3 is an irrational number

proved.

Answer 2

Given :-

√3 is an irrational number

To Prove :-

5 - √3 is an irrational number

Solution :-

Consider 5 - √3 be a rational number

We can write this rational number as p/q form where q not equal to zero

5 - √3 = p/q

5 - p/q = √3

(5q - p)/q = √3

Since , both p and q are integers

Now ,

(5p - q)/q is a rational number and  √3 is also a rational number

But our assumption is wrong because √3 is an irrational number

Thus , 5 - √3 is an irrational number

Hence , proved