Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.5 Real Numbers and Their Properties; Clock Addition - Exercise Set 5.5: 49

Answer

$\sqrt3 \cdot \sqrt{12} = \sqrt{36} = 6$ $\sqrt3$ and $\sqrt{12}$ are irrational numbers, but 6 is not.

Work Step by Step

Irrational numbers are not closed with respect to multiplication, as can be seen in the example below: $\sqrt3$ and $\sqrt{12}$ are irrational numbers. However, $\sqrt3 \cdot \sqrt{12} = \sqrt{36}=6$, which is not an irrational number.
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