Question

Show that 3 +2 root 5 is an irrational number.​

Answer 1

Answer:

let us assume 3 + 2√5 is a rational number.

3 + 2√5 = a/b (where a and b are integers and a ≠ 0)

2√5 = a/b - 3

2√5 = a - 3b/ b

√5 = a - 3b/ 2b

a - 3b/ 2b is rational.

√5 = a - 3b/ 2b and hence √5 is also rational.

but this contradicts the fact that √5 is irrational.

hence proved, 3 + 2√5 is irrational.

Answer 2

Answer:

irrational no.

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