Question

Prove that ( 5 -2√3 ) is an irrational number.​

Answer 1

Answer:

let us assume 5-2✓3 is rational

5-2✓3 = p/q [where p and q are Integers]

5-p/q = 2✓3

2✓3 = 5q-p/q

✓3 = 5q-p/q × 1/2

✓3 = 5q-p/2q

No we know That ✓3 is a irrational, We also know that 5q-p/2q is a rational no.

So this contradicts the fact that Rational and irrational can not be equal

And Hence, 5-2✓3 Is a irrational no.