Question

1. the sum of two rational numbers is always always a (irrational number / rational number)

2. the sum of two irrational numbers is always (irrational number / rational number )

3. the sum of a rational number and a irrational number is always a (irrational number / rational number )

Answer 1

One

The sum of two rational numbers is always rational. sqrt(9) + sqrt(25) = 3 + 5 which is rational. sqrt(16/100) = 4/10 = 2/5 is also rational. 3/28 is rational as well.

Two

Those are irrational. sqrt(10) + pi = ???? You cannot reduce this to any kind of fraction. Two irrationals always give a rational.

Three

The irrational number controls the answer. 10 + sqrt(5) is irrational. The 10 is OK. It is raional, but sqrt(5) is not a rational number.