<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-real-number-properties-iii" target="_blank">Real Number Properties III Exercise</a></p><p>Whenever you're completing operations on real numbers, we need to keep in mind several <strong><span style="color:#27ae60;">Real Number Properties</span></strong>:</p>
<ul>
<li><span style="color:#e74c3c;">Property 9</span>: If the product of two numbers is negative, exactly one of the two numbers is negative. </li>
<li><span style="color:#e74c3c;">Property 10</span>: The absolute value of the sum of two integers is always less than or equal to the sum of the absolute values of the two integers. That is, $$|a + b| \leq |a| + |b|$$</li>
<li><span style="color:#e74c3c;">Property 11</span>: The absolute value of the product of two integers is equal to the product of the absolute values of the two integers. That is, $$|ab| = |a||b|$$</li>
<li><span style="color:#e74c3c;">Property 12</span>: If $a = 1$, $$a = a^2 = \sqrt{a}$$ while if $a > 1$, $$a^2 > a > \sqrt{a}$$ and if $a < 1$, $$\sqrt{a} > a > a^2$$</li>
</ul>