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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.

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Answer: False.

Step-by-step 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.

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