Question

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

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Assume that 2-5√3 is rational.

So, 2-5√3 = a/b where a and b are integers and co-primes.

2-5√3 = a/b

5√3 = 2 - a/b

5√3 = 2b-a/b

√3 = 2b-a / 5b

Since product and difference of integers are integers,

2b-a / 5b is rational

but we know that √3is irrational

so this is a contradiction

⇒our assumption is wrong

⇒ 2- 5√3 is irrational.

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