In this video, we are going to simplify simple radical expressions. Note that a perfect square number has a rational square root.

because ,

because ,

because , and so on…

There are other radical expressions other than perfect square ones, to which they may not have a rational square root.

and , and are some examples.

However, having an irrational square doesn’t mean that the radical expression cannot be simplified.

cannot be simplified because it is in its simplest state.

For , *4* and *5* are factors of *20*. Choosing factors that are perfect squares make the simplifying process easier.

=

is 2, so is really just

For , *4* and *8* are factors of *32*.

=

is 2, so is

can be further simplified into and , or

In the end, is

Another way of simplifying is to use and as the factors.

Since 16 is a perfect square, can be written as , leading to the answer immediately.

Now let’s try three more examples:

*25* is a perfect square that goes into *75* and the other factor is *3*

The square root of *25* is *5* so the final answer is

*4* and *12* go into 48

can be broken down into *2* and can be broken down into and

The square root of *4* is *2**, *, so we have

Now let’s do the same problem by using the perfect square

*16* is a perfect of *48* and the accompanying factor is *3
*The square root of

*16*is

*4*, so we have , same answer

*9* is a perfect square that goes into *63* and the other factor is *7*

The square root of *9* is *3* so the final answer is

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