Simplify Square Root of 8427

Here we will show you two methods that you can use to simplify the square root of 8427. In other words, we will show you how to find the square root of 8427 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.

√8427 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 8427 to simplify the square root of 8427. 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 8427. The factors of 8427 are 1, 3, 53, 159, 2809, and 8427. Furthermore, the greatest perfect square on this list is 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Calculate 8427 divided by the greatest perfect square from the list of all factors of 8427. We determined above that the greatest perfect square from the list of all factors of 8427 is 2809. Furthermore, 8427 divided by 2809 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 8427 in its simplest radical form as follows:

√8427 = A√B

√8427 = 53√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 8427 to simplify the square root of 8427 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 8427 and then take the square root of that product. The prime factors that multiply together to make 8427 are 3 x 53 x 53. When we strip out the pairs only, we get 53 x 53 = 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Divide 8427 by the number (A) squared. 53 squared is 2809 and 8427 divided by 2809 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 8427 in its simplest radical form as follows:

√8427 = A√B

√8427 = 53√3

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Simplify Square Root of 8428
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