Simplify Square Root of 54405

Here we will show you two methods that you can use to simplify the square root of 54405. In other words, we will show you how to find the square root of 54405 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√54405 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54405 to simplify the square root of 54405. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 54405. The factors of 54405 are 1, 3, 5, 9, 13, 15, 27, 31, 39, 45, 65, 93, 117, 135, 155, 195, 279, 351, 403, 465, 585, 837, 1209, 1395, 1755, 2015, 3627, 4185, 6045, 10881, 18135, and 54405. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 54405 divided by the greatest perfect square from the list of all factors of 54405. We determined above that the greatest perfect square from the list of all factors of 54405 is 9. Furthermore, 54405 divided by 9 is 6045, therefore B equals 6045.

Now we have A and B and can get our answer to 54405 in its simplest radical form as follows:

√54405 = A√B

√54405 = 3√6045

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54405 to simplify the square root of 54405 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 54405 and then take the square root of that product. The prime factors that multiply together to make 54405 are 3 x 3 x 3 x 5 x 13 x 31. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 54405 by the number (A) squared. 3 squared is 9 and 54405 divided by 9 is 6045. Therefore, B equals 6045.

Once again we have A and B and can get our answer to 54405 in its simplest radical form as follows:

√54405 = A√B

√54405 = 3√6045

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