Question

given root 2 is irrational proof that 5 + 3 root 2 is an irrational number

Answer 1

Heya !!!


If possible , suppose 5+3✓2 is rational Number.


Therefore,


5+3✓2 = A/B , where a and b are Integers and b not equal 0


=> 3✓2 = 5 - A/B


=> ✓2 = 5/3 - A/3B = Rational - Rational = Rational.


=> Irrational ✓2 = Rational , which is not possible so our SUPPOSITION is wrong.



Hence,


5+3✓2 is irrational Number.



HOPE IT WILL HELP YOU...... :-)