Question

Given ✓2 is irrational proove that (5+3✓2) is irrational

Answer 1

Given ✓2 is irrational.
Rational * irrational = irrational.
So 3✓2 is irrational.

Irrational + rational = irrational.
So 5+3✓2 is irrational number.
Pls make me as brainliest...

Answer 2

5+3√2 is a rational nmbr....
then it is of the form a/b where a and b are co-primes and b≠0
3√2=a/b-5=a-5b/b
√2=a-5b/3b
since a and b are integers ,so a-5b/3b is rational .....
but it is given that √2 is irrational...so the equality cannot exist
this is because of our contradictory assumption that 5+3√2 is rational....
hence,5+3√2 is an irrational number

hope this helps you