Question

Prove that 3+√5 is an irrational number i need full explanation plzz urgent plz

Dont dare to spam gyanji here​

Answer 1

Answer:

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

Answer 2

let us assume that 3+ underroot 5 is a rational number.

3+underroot 5 = a/b ( here a and b are coprime number)

underroot 5 = a/b - 3 ( take LCM)

underroot 5 = a - 3b / b

here a - 3b /b is also a rational number

so our assumption is wrong

3+underroot 5 is an irrational number...

I am also in class 10th

please don't do upper answer in exam it is wrong because you are asking (3+ underroot 5 ) not (3+ 2 underoot 5 )