01Eaddingsurds

= Adding & Subtracting Surds = toc

Adding Algebra
Recall that in algebra, we can only add and subtract __**like**__ terms. math \\ \textbf{(a)} \quad 3xy + 5xy = 8xy \\ \\ \textbf{(b)} \quad 5a +7b + 3a - b = 8a + 6b math

Adding Surds
Exactly the same rules apply with surds.

Surds can only be added or subtracted if the root part of the surd is the same (ie they are __**like**__ surds).

** Example 1 **
math \textbf{(a)} \quad 3 \, \sqrt{7} \; + 5\, \sqrt{7} \; = 8\, \sqrt{7} math

math \textbf{(b)} \quad \sqrt{5} \; + 6\, \sqrt{10} \; + \sqrt{5}\; - 2\, \sqrt{10} = 2\, \sqrt{5} \; + 4\, \sqrt{10} math

Simplifying then Adding
Sometimes you will need to simplify surds before you can add them

** Example 2 **
math \\ 6\, \sqrt{12} \; + \; 2\,\sqrt{27} \; = 6 \times \sqrt{4} \times \sqrt{3} \;\; + \;\; 2 \times \sqrt{9} \times \sqrt{3} \\ \\ . \qquad \qquad \qquad \;\; = 6 \times 2\,\sqrt{3} \;\; + \;\; 2 \times 3\,\sqrt{3} \\ \\ . \qquad \qquad \qquad \;\; = 12\,\sqrt{3} \;\; + \;\; 6\,\sqrt{3} \\ \\ . \qquad \qquad \qquad \;\; = 18\,\sqrt{3} math Go to top of page flat .