Simplify Square Root of 58401

Here we will show you two methods that you can use to simplify the square root of 58401. In other words, we will show you how to find the square root of 58401 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.

√58401 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58401 to simplify the square root of 58401. 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 58401. The factors of 58401 are 1, 3, 7, 9, 21, 27, 63, 81, 103, 189, 309, 567, 721, 927, 2163, 2781, 6489, 8343, 19467, and 58401. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 58401 divided by the greatest perfect square from the list of all factors of 58401. We determined above that the greatest perfect square from the list of all factors of 58401 is 81. Furthermore, 58401 divided by 81 is 721, therefore B equals 721.

Now we have A and B and can get our answer to 58401 in its simplest radical form as follows:

√58401 = A√B

√58401 = 9√721

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58401 to simplify the square root of 58401 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 58401 and then take the square root of that product. The prime factors that multiply together to make 58401 are 3 x 3 x 3 x 3 x 7 x 103. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 58401 by the number (A) squared. 9 squared is 81 and 58401 divided by 81 is 721. Therefore, B equals 721.

Once again we have A and B and can get our answer to 58401 in its simplest radical form as follows:

√58401 = A√B

√58401 = 9√721

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Simplify Square Root of 58402
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