Question

Given positive irrational numbers a, b, and c, which of the following must also be irrational?

A. abc
B. a + b + c
C. ab/c
D. a^2 + b^3 + c^4
(Select all correct answers)

Answer 1

The expressions 'abc', 'a + b + c', and 'ab/c' must be irrational.

Step-by-step explanation:

To determine which of the given expressions must also be irrational, we need to understand the properties of irrational numbers.

An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. It cannot be written as a terminating or repeating decimal.

Given three positive irrational numbers, the following expressions must also be irrational:

1. abc: The product of three irrational numbers will also be irrational, as the product of rational and irrational numbers is irrational.
2. a + b + c: The sum of three irrational numbers can also be irrational, as the sum of rational and irrational numbers can be irrational.
3. ab/c: The division of two irrational numbers can also be irrational.

Therefore, the correct answers are options A, B, and C.