# Simplifying Square Roots

To simplify a square root: make the number inside the square root as small as possible (but still a whole number):

### Example: √12 is simpler as 2√3

Get your calculator and check if you want: they are both the same value!

Here is the rule: when a and b are **not negative**

And here is how to use it:

### Example: simplify √12

12 is 4 times 3:

Use the rule:

And the square root of 4 is 2:

So √12 is simpler as 2√3

### Example: simplify √45

So √45 is simpler as 3√5

Another example:

### Example: simplify √8

(Because the square root of 4 is 2)

And another:

### Example: simplify √18

√18 = √(9 × 2) = √9 × √2 = 3√2

It often helps to factor the numbers (into prime numbers is best):

### Example: simplify √6 × √15

First we can combine the two numbers:

Then we factor them:

Then we see two 3s, and decide to "pull them out":

## Fractions

There is a similar rule for fractions:

### Example: simplify √30 / √10

First we can combine the two numbers:

Then simplify:

## Some Harder Examples

### Example: simplify \frac{√20 × √5}{√2}

See if you can follow the steps:

### Example: simplify 2√12 + 9√3

First simplify 2√12:

Now both terms have √3, we can add them:

## Surds

Note: a root we **can't** simplify further is called a Surd. So √3 is a surd. But √4 = 2 is not a surd.