Simplify Square Root of 12427

Here we will show you two methods that you can use to simplify the square root of 12427. In other words, we will show you how to find the square root of 12427 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.

√12427 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12427 to simplify the square root of 12427. 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 12427. The factors of 12427 are 1, 17, 43, 289, 731, and 12427. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 12427 divided by the greatest perfect square from the list of all factors of 12427. We determined above that the greatest perfect square from the list of all factors of 12427 is 289. Furthermore, 12427 divided by 289 is 43, therefore B equals 43.

Now we have A and B and can get our answer to 12427 in its simplest radical form as follows:

√12427 = A√B

√12427 = 17√43

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12427 to simplify the square root of 12427 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 12427 and then take the square root of that product. The prime factors that multiply together to make 12427 are 17 x 17 x 43. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 12427 by the number (A) squared. 17 squared is 289 and 12427 divided by 289 is 43. Therefore, B equals 43.

Once again we have A and B and can get our answer to 12427 in its simplest radical form as follows:

√12427 = A√B

√12427 = 17√43

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Simplify Square Root of 12428
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