Math, asked by rzubaid8, 9 months ago

Prove that 3+2√5 is an irrational number .​

Answers

Answered by HA7SH
19

Step-by-step explanation:

Given:3 + 2√5

To prove:3 + 2√5 is an irrational number.

Proof:

Letus assume that 3 + 2√5 is a rational number.

Soit can be written in the form a/b

3 + 2√5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving3 + 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 But √5 is an irrational number.

so it contradictsour assumption.

Our assumption of3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

Hence proved

Answered by Vaibthegreat
1

we know a property that

When rational is added to irrational then we get a irrational number.

So 3 is a rational and 2root 5 is irrational

so According to the property given up

3 + 2root5 is a irrational number

Therefore proved

Similar questions