Question

Prove that 3 + 2√5 is irrational.​

Answer 1

Since , we know that √5 is an irrational number. So, the number added or subtracted to an irrational number is also irrational number.

itzDopeGirl

Answer 2

Answer:

By Contradiction Method,

Let us assume that 3+2√5 is rational.

$3 + 2 \sqrt{5} = \frac{x}{y} \\ 2 \sqrt{5} = \frac{x}{y} - 3 \\ 2 \sqrt{5} = \frac{x - 3y}{y} \\ \sqrt{5} = \frac{x - 3y}{2y}$

RHS is rational.

LHS us irrational.

It contradicts. Our supposition was wrong.

3+2√5 is irrational.

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