Question

Given √3 is irrational, prove that 3+2√3 is a irrational number ​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Thank you too mate! Here's your answer:

Step-by-step explanation:

Let 3 + 2√3 = a/b, where a and b are co-prime.

(3 + 2√3)² = a²/b²

3² + 2(2√3)(3) + (2√3)² = a²/b²

9 + 12√3 + 12 = a²/b²

12√3 = (a²/b² - 21)

√3 = (a²/b² - 21) / 12.

Observe that we have an irrational number (Given) on the LHS and a rational number in the RHS.

But an irrational number can never be equal to a rational number.

So our assumption was wrong.

Hence it's proved that 3 + 2√3 is an irrational number.

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