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}

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

flashcards

QuestionAnswer
a\sqrt{x}\times b\sqrt{y}=(a\times b)\sqrt{xy}$Multiply coefficients together (a × b) and radicands together (x × y), then simplify if possible.
2\sqrt{3}\times4\sqrt{5}(2\times4)\sqrt{3\times5}=8\sqrt{15}
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}