Question

48 sum or product the timing was the result is a rational number or irrational

Answer 1

a)

`2+√(21)`

The result is irrational!

Because the sum of a rational and an irrational number is always irrational.

b)

`(10)/(19)+(5)/(13)`

The result is rational!

The sum of two rational numbers is always rational. You can justify it by doing:

`k=(a)/(b)+(c)/(d)=(ad+bc)/(bd)\Rightarrow k\in\mathbb{Q}`

c)

`√(14)\cdot18`

The result is irrational!

In fact, the product of an irrational and a rational will always be irrational.,

d)

`15\cdot(9)/(16)`

The result is rational!

The product of two rational numbers is always rational