Question

show that 3 root 2 + root 5 is an irrational number

Answer 1

Le us assumed that 3√2+√5 is a rational number and can be written in the form of p/q.where p and q are integers and q is not equal to 0.

3√2+√5= p/q

3√2 = p/q-√5

3√2 = p - √5q/q

√2 = p- √5q/3q

Therefore p is a rational number

Also -√5 is a rational number

And 3q is a rational number

So, p- √5q/3q is rational number

LHS = RHS.

But, we know that √2 is an irrational number.so, it is not possible and our assumption wrong.

3√2+√5 is irrational number.

HOPE IT HEP YOU....