Question

show that 5-√3is irrational
step by step need correct answer​

Answer 1

Answer:

let us assume to the contrary that 5-root3 is rational

=>5-root3=a/b     (where a and b are co primes and b not equal to zero)

=>root3=5b-a/b

Here a and b are integers, so 5-a/b is rational , hence root3 is also rational.

But this contradicts our fact that root 3 is irrational.

This contradiction has arisen because of our incorrect assumption that 5-root3 is rational.

hence 5-root3 is irrational

Step-by-step explanation:

Have a nice day my dear friend :)

Answer 2

let us assume to the contrary that 5-root3 is rational

=>5-root3=a/b     (where a and b are co primes and b not equal to zero)

=>root3=5b-a/b

Here a and b are integers, so 5-a/b is rational , hence root3 is also rational.

But this contradicts our fact that root 3 is irrational.

This contradiction has arisen because of our incorrect assumption that 5-root3 is rational.

hence 5-root3 is irrational

Step-by-step explanation:

Have a nice day my dear friend :)