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,
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.