Question

Show that √5+√3is a irrational number given that positive square root of15 is an irrational number

Answer 1

Answer:

Call the given number x.

Then x² = 5 + 2√5√3 + 3 = 8 + 2√(15).

If x were rational, then x² would be rational, x²-8 would be rational, and finally, (x²-8)/2 would be rational.

But (x²-8)/2 = √(15), which we are told is irrational.

Therefore x is irrational after all.