Question

Q21) Prove that 5-2√3 is an irrational number,​

Answer 1

5 - 2 √3 = p/q, where p and q are integers, having no common factor except 1 and q ≠ 0. ... Therefore, √3 is also a rational number, which contradicts our assumption. Thus, Our supposition is wrong. Hence, 5 - 2 √3 is an irrational number.

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Answer 2

Answer:

Step-by-step explanation:

Let us assume that 5 - 2 √3 is a rational number.

So, 5 - 2 √3 may be written as

5 - 2 √3 = p/q, where p and q are integers, having no common factor except 1 and q ≠ 0.

⇒ 5 - p/q = 2 √3

⇒ √3 = 5q - p/2q

Since, 5q - p/2q is a rational number as p and q are integers.

Therefore, √3 is also a rational number, which contradicts our assumption.

Thus, Our supposition is wrong.

Hence, 5 - 2 √3 is an irrational number.