Question 2

Prove that 3 + 2√5 is irrational.

Answer

Let us assume 3 + 2√5 is a rational number.
Therefore, 3 + 2√5 = p/
q where p and q are co primes and q ≠ 0.

3 + 2√5 = ab           

On solving, 2√5 =(a/b) - 3

√5 =1/2 (a/- 3)

Since a, b are integers and 1/2 (a/b-3 ) is also a rational number.
But we know √5 is an irrational number.
Thus our assumption is wrong. 3 + 2√5 is not a rational number.
Hence proved.

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