Question

What number squared is 54?

Answer 1

`54` is not a perfect square, but `3sqrt6` is the simplified radical form of the number.

Explanation:

We can still put `54` under the square root sign and simplify that to get a value.

Perfect squares: Numbers are the product of a number and itself, for example: `4` is a perfect square since `2 * 2` equals `4`.

`sqrt54`

We need to find factors of `54` that are perfect squares . With a little bit of guess and check if you did not know this already, `54` is divisible by `9` , and `9` is a perfect square (`3 * 3`).

So lets divide `54` by 9 to find the other factor. We get `6` (`6 * 9 = 54`). Now we need to put `54` into a 'tree' to simplify the factors down.:

                                       54 
                                      /    \ 
                                  9         6
                                /   \       /   \
                             3       3 3      2

Here I broke down the `54` into the smallest factors. We have `3` and `3` for `9`, and `2` and `3` for `6`. This is how you would write the simplified radical form of the square:

There are two `3`s, so just take one. You have two different numbers under `6`, so multiply them. Take your first number, put it before the radical sign:

`3sqrt`

Now take the product of the two numbers and put it inside the radical:

`3sqrt6`

And that is how you get a square in radical form. I am aware this did look a bit confusing, and it is easier than I put it. Please ask me if you have any questions.