Another best question of irrational number of class 10th . How can we solve this question . Please give me some suggestion for this question. The best way for solving this question. Prove that 3 + 2√5 + is irrational.

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Let us assume 3 + 2

√5 is rational.Then we can find co-prime x and y (y ≠ 0) such that 3 + 2√5 = x/y

Rearranging, we get,

Since, x and y are integers, thus,

is a rational number.

Therefore,

√5 is also a rational number. But this contradicts the fact that√5 is irrational.So, we conclude that 3 + 2

√5 is irrational.