<ol class="num-list"><li data-list-item-id="item-1780991256719-pduw54ki4"><div class="list-item-paragraph"> \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \)</div></li><li data-list-item-id="item-1780991257204-sx8zs0s3s"><div class="list-item-paragraph"> \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \)</div></li><li data-list-item-id="item-1780991257652-im3ml54br"><div class="list-item-paragraph">\(\sqrt{a} \times \sqrt{a} = \sqrt{a^2} = a\)</div></li></ol>
<p>*Note the above laws of surds do not apply to addition and subtraction<br>\(\sqrt{a} + \sqrt{b} \neq \sqrt{a + b} \text{ and}\hspace{0.5em} \sqrt{a} - \sqrt{b} \neq \sqrt{a - b} \)</p>
<ol class="num-list" start="4"><li data-list-item-id="item-1780991292153-ni2iptjf0"><div class="list-item-paragraph">\(p\sqrt{a} + q\sqrt{a} = (p + q)\sqrt{a}\)<br>Example: \(5\sqrt{2} + 2\sqrt{2} = 7\sqrt{2}\)</div></li><li data-list-item-id="item-1780991293385-0emkxebc9"><div class="list-item-paragraph">\(p\sqrt{a} - q\sqrt{a} = (p - q)\sqrt{a}\)<br>Example: \(9\sqrt{5} - 3\sqrt{5} = 6\sqrt{5} \)</div></li></ol>

 \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \)

 \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \)

\(\sqrt{a} \times \sqrt{a} = \sqrt{a^2} = a\)

*Note the above laws of surds do not apply to addition and subtraction
\(\sqrt{a} + \sqrt{b} \neq \sqrt{a + b} \text{ and } \sqrt{a} - \sqrt{b} \neq \sqrt{a - b} \)

\(p\sqrt{a} + q\sqrt{a} = (p + q)\sqrt{a}\)
Example: \(5\sqrt{2} + 2\sqrt{2} = 7\sqrt{2}\)

\(p\sqrt{a} - q\sqrt{a} = (p - q)\sqrt{a}\)
Example: \(9\sqrt{5} - 3\sqrt{5} = 6\sqrt{5} \)

Laws of Surds

Laws of Surds