Question

prove that √3 + √5 is an irrational number, given that √3 is irrational​

Answer 1

Answer:

assume that √3+√5 be rational

so we can say that √3+√5 will be p/q

now, √3= p/q-√5

√3=p-√5q/q

squaring both the sides

3= p²-2√5pq+5q/q²

3q²=p-2√5pq+5q

3q²-p-5q/pq=√5

the LHS is a  rational number as it is of the form p/q how ever we are seeing that the RHS is an irrational number.

SO ACCORDINGLY A RATIONAL NUMBER CAN NEVER BE EQUAL TO AN IRRATIONAL NUMBER.

Step-by-step explanation: