Question

Which of the following shows that the sum of two irrational numbers can be irrational?

A. √3 + √5
B. (3 + √5) + (3 – √5)
C. (5 + √7) + (3 – √7)
D. 5 +(-5)

Answer 1

The sum of two irrational numbers can be irrational if the irrational numbers have different radicands.

Step-by-step explanation:

The sum of two irrational numbers can be irrational if the irrational numbers have different radicands (the number inside the square root).

Option A, √3 + √5, is an example of the sum of two irrational numbers that is irrational.

When you add √3 + √5, you cannot simplify the expression any further because the radicands are different. Therefore, the sum (√3 + √5) is irrational.