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