Simplify Square Root of 93474

Here we will show you two methods that you can use to simplify the square root of 93474. In other words, we will show you how to find the square root of 93474 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.

√93474 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93474 to simplify the square root of 93474. 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 93474. The factors of 93474 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 577, 1154, 1731, 3462, 5193, 10386, 15579, 31158, 46737, and 93474. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 93474 divided by the greatest perfect square from the list of all factors of 93474. We determined above that the greatest perfect square from the list of all factors of 93474 is 81. Furthermore, 93474 divided by 81 is 1154, therefore B equals 1154.

Now we have A and B and can get our answer to 93474 in its simplest radical form as follows:

√93474 = A√B

√93474 = 9√1154

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93474 to simplify the square root of 93474 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 93474 and then take the square root of that product. The prime factors that multiply together to make 93474 are 2 x 3 x 3 x 3 x 3 x 577. 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 93474 by the number (A) squared. 9 squared is 81 and 93474 divided by 81 is 1154. Therefore, B equals 1154.

Once again we have A and B and can get our answer to 93474 in its simplest radical form as follows:

√93474 = A√B

√93474 = 9√1154

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Simplify Square Root of 93475
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