4. Addition and Subtraction of Radicals

In algebra, we can combine terms that are similar eg.

2a + 3a = 5a

8x2 + 2x − 3x2 = 5x2 + 2x

Similarly for surds, we can combine those that are similar. They must have the same radicand (number under the radical) and the same index (the root that we are taking).

Example 1

(a) 2√7 − 5√7 + √7

(b) `root(5)6+4root(5)6-2root(5)6`

(c) `sqrt5+2sqrt3-5sqrt5`

Example 2

(a) `6sqrt7-sqrt28+3sqrt63`

(b) `3sqrt125-sqrt20+sqrt27`

Example 3

Simplify:

`sqrt(2/(3a))-2sqrt(3/(2a)`

Exercises

Q1 `sqrt7+sqrt63`

Q2 `2sqrt44-sqrt99+sqrt2sqrt88`

Q3 `root(6)sqrt2-root(12)(2^13)`

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