Question

prove that 5-√3 is an irrational number​

Answer 1

Hey friend!! :)))

Suppose 5-√3 is rational

5-√3=p/q, where p and q are co-primes

therefore..

-√3=p/q+5

LHS=Irrational and RHS =Rational

Hence proved...

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Answer 2

Answer:

Let 5 - √3 be rational,

Then, 5 - √3 can be expressed as where, p and q are co-prime integers and

q ≠ 0,

we have,

(picture)

As p and q are integers, 5q - p is also an integer

is a rational number.

But √3 is an irrational number, so the equality is not possible.

This contradicts our assumption, that 5 - √3 is a rational number.

Therefore, 5 - √3 is an irrational number.