Question

Prove that 3 + 2/5 is irrational​

Answer 1

$\sf{ \orange { \underline { \underline { To \:Prove \: - }}}}$

• 3 + 2√5 is an irrational number.

$\sf{ \purple { \underline { \underline { PROOF↓ \: - }}}}$

→Let us assume that 3 + 2√5 is a rational number.

→So, it can be written in the form a/b

3 + 2√5 = a/b

→Here a and b are coprime numbers and b ≠ 0

Solving 3 + 2√5 = a/b we get,

=>2√5 = a/b – 3

=>2√5 = (a-3b)/b

=>√5 = (a-3b)/2b

→This shows (a-3b)/2b is a rational number. But we know that √5 is an irrational number.

→So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number.

[Hence proved!!]

Answer 2

Step-by-step explanation:

Prove that 3 + 2V5 is irrational.

We have to prove 3 + 2V5 is irrational

Let us assume the opposite,

i.e., 3 + 2/5 is rational

Hence, 3 + 2V5 can be written in the form-

where a and b (b# 0) are co-prime (no common factor other than 1)

Hence, 3 + 2/5 = b

2V5 = - 3

2V5 = " a - 3b b