Prove that √3 + √5 is irrational.

Let be any rational number x

squaring both sides

as x is a rational number so x² is also a rational number, 8 and 2 are rational nos. , so √15 must also be a rational number as the quotient of two rational numbers is rational

but, √15 is an irrational number

We arrive at a contradiction this shows that our supposition was wrong

so √3 + √5 is not a rational number.

Hence, proved.