# Square Roots - What are they?

## Square Roots, What are they? - How it Works - Video

### Example 1

Example 1:

A square root of a number is a value that, when multiplied by itself, gives the number. What does that mean?

We first need to find the factor pairs of the number under the square root sign, and in this case 4, where 4 is a square number.

The factor pairs of 4 are 1*4 and 2*2. And 2*2 forms a perfect square. Hence the square in the square root.

2 is being multiplied by itself to give the number 4, also a square number.

So 2 is the root of 4.

### Example 2

Example 2:

A square root of a number is a value that, when multiplied by itself, gives the number. What does that mean?

We first need to find the factor pairs of the number under the square root sign, and in this case 9, where 9 is a square number.

The factor pairs of 9 are 1*9 and 3*3. And 3*3 forms a perfect square. Hence the square in the square root.

3 is being multiplied by itself to give the number 9, also a square number.

So 3 is the root of 9.

### Example 3

Example 3:

A square root of a number is a value that, when multiplied by itself, gives the number. What does that mean?

We first need to find the factor pairs of the number under the square root sign, and in this case 16, where 16 is a square number.

The factor pairs of 16 are 1*16 and 2*8 and 4*4. And 4*4 forms a perfect square. Hence the square in the square root.

4 is being multiplied by itself to give the number 4, also a square number.

So 4 is the root of 16.

### Can Square Roots be Negative?

YES.

The roots in the picture above are the principal square roots or the positive roots of the number.

In order for the root to be negative, we need to use the square root as an inverse of an equation. For example, x^{2 }= 9. Where we x can equal 3 or -3, because 3 * 3 = 9 and -3 * -3 = 9.

## Live Worksheet

Here is the link if you prefer.