Question

prove 5+3✓2 is irrational​

Answer 1

Given : 5 + 3√2

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

Proof:

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

Soit can be written in the form a/b

5 + 3√2 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving 5 + 3√2 = a/b we get,

=> 3√2 = a/b – 5

=> 3√2 = (a-5b)/b

=> √2 = (a-5b)/3b

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

so it contradicts our assumption.

Our assumption of 5 + 3√2 is a rational number is incorrect.

5 + 3√2 is an irrational number

Hence proved