Question

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

Answer 1

Question:

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

Solution:

Let,

5-2√3 be a rational number.

5-2√3 = p/q 【where p & q are integers, q ≠ 0 & q is co-prime number】

→ $-2 \sqrt{3} = \frac{p}{q} = 5$

→ $-2 \sqrt{3} = p - \frac{5q}{q}$

→ $\sqrt{3} = \frac{p-5q}{-2q}$

We know that, p/q is a rational number.

Therefore,

• √3 is also a rational number.
• 5-2√3 is an irrational number.