Multiplying surds

When multiplying surds, we can multiply the numbers outside the surds and the numbers inside the surds separately.

This can be written as:

a\sqrt{x}\times b\sqrt{y}=(a\times b)\sqrt{xy}

Example: simplify 2\sqrt{3}\times4\sqrt{5}

• =(2\times4)\sqrt{3\times5}
• =8\sqrt{15}

Example: simplify 3\sqrt{2}\times5\sqrt{6}

• =(3\times5)\sqrt{2\times6}
• =15\sqrt{12}
• =15\sqrt{4\times3}
• =15\times2\sqrt{3}
• =30\sqrt{3}