Question

17. Show that 5-√3 is irrational.​

Answer 1

Answer:

Let 5-√3 is a rational number

Let 5-√3=a/b (where a and b are integers)

-√3=a/b-5

5-a/b=√3

5b-a/b=√3

If LHS is rational number then its RHS is also rational number.

So √3 is a rational number.

But it is the fact that √3 is irrational number.

So our supposition/assumption is wrong.

Hence, 5-√3 is irrational number.