Question

. Prove that 3 + 2√5 is irrational
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Answer 1

Answer:

3+2√5

5√5

the root cannot be rational

so the above equation is irrational

Answer 2

Answer:

→ let take that 3+2√5 is rational number

→ so, we can write this answer as

⇒3+2√5 = a/b

Here a & b use two coprime number and

b ≠ 0.

$⇒2 \sqrt{5} = \frac{a}{b}$

$⇒2 \sqrt{5} = \frac{a - 3b}{b}$

$\sqrt{5} = \frac{a - 3b}{2b}$

Here a and b are integer so

$\frac{a - 3b}{2b}$

is a rational number

so

√5 should be rational number but

√5 is a irrational number so it is contradict

- Hence 3+2√5 is irrational.