Question

prove that (3+2√5)² is irrational number.​

Answer 1

$(3+2 \sqrt{5} )² = {3}^{2} + {(2 \sqrt{5)} }^{2} + 2 \times 3 \times 2 \sqrt{5} \\ = 9 + 20 + 12 \sqrt{5} \\ = 29 + 12 \sqrt{5}$

Since, √5 is an irrational number and sum of rational and irrational number is always irrational.

Therefore, (3+2√5)² is ir irrational number