Question

PLEASE HELP THANK YOU SO MUCH Consider the statement.

The sum of two irrational numbers is always an irrational number.

Is the statement true or false? Justify your answer.

true; Irrational numbers are closed under addition: + 27 = 37.

false; Only division results in irrational numbers. All other operations on real numbers give rational numbers.

true; The sum of two irrational numbers is a rational number, which is also an irrational number since all rational numbers are also irrational

numbers.

false; Irrational numbers are not closed under addition: V14 + (-14) = 0.

Answer 1

Answer: False.

Explanation:

The statement is:

"The sum of two irrational numbers is always an irrational number."

We know that √2 is an irrational number.

Then the opposite number, (-1)*√2 is also an irrational number.

Then we can sum two irrational numbers like:

√2 + (-√2) = 0

and 0 is a rational number.

Then we have found a counter-example, which means that the statement is false.