Question

How can you determine if a square root is completely simplified?

Answer 1

Answer:

It cannot be divided by any number and equal a whole number.

Step-by-step explanation:

Okay, so I'm going to give an example of the simplifying process.

$\sqrt{243}$

If you were to just type this in to a calculator you would get 15.58 and so on, so that means we have to just simplify instead of solving for accuracy purposes.

So take 243 and divide it by a number that can go into it equally. I'm going use 3. When you do that you get 81. Usually when I do this I draw it out to better see it, so I'm going to try for you. The 3 is prime so we can't simplify that term anymore, but you can still simplify the 81, so that is what we do next. I'm going to use 3 to make it easier in the end results. Notice 3 is prime but 27 still is not, so we repeat this process again. I'm gonna stick with 3. Now simplify the 9.

                 243

3                                     81

                                3            27

                                           3      9

                                                  3    3

For every pair of number we have that are the same we get to put one outside the sqareroot sign (I know that sounds confusing). Start by listing them like this.

3 x 3 x 3 x 3 x 3

Now organize into groups of two.

(3x3)(3x3)(3)   Notice we have two groups that are paired. This means we can take two 3's and bring them outside the squareroot sign. Like this

$3x3\sqrt{3}$  

$9\sqrt{3}$

The lone 3 just goes back in the squareroot. once you can't find a number to divide the number inside the sign by you have simplified the expression completely. Hope that makes some sense