Add and Subtract Surds

 Surds are a way of writing irrational numbers using rational numbers and square roots.

The rule of adding and subtracting surds is that the rational number under the square root must be the same. This is similar to simplifying algebraic expressions.

For example:

√5 + √5

= 2√5

Example 2

9√5 - 4√5

= 5√5

But what do we do if the values are different?

If the values under the square root sign are different, we would need to simplify the surd so they have the same value.

Example

Simplify √12 + √3

First, we simplify √12

√12 = √4 x √3 = 2 x √3 = 2√3

Now we can simplify.

2√3 + √3

= 3√3

Does that make sense?