# 4. Addition and Subtraction of Radicals

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

2

a+ 3a= 5a8

x^{2}+ 2x− 3x^{2}= 5x^{2}+ 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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