Simplify Square Root of 93552

Here we will show you two methods that you can use to simplify the square root of 93552. In other words, we will show you how to find the square root of 93552 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.

√93552 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 93552 to simplify the square root of 93552. 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 93552. The factors of 93552 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1949, 3898, 5847, 7796, 11694, 15592, 23388, 31184, 46776, and 93552. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 93552 divided by the greatest perfect square from the list of all factors of 93552. We determined above that the greatest perfect square from the list of all factors of 93552 is 16. Furthermore, 93552 divided by 16 is 5847, therefore B equals 5847.

Now we have A and B and can get our answer to 93552 in its simplest radical form as follows:

√93552 = A√B

√93552 = 4√5847

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 93552 to simplify the square root of 93552 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 93552 and then take the square root of that product. The prime factors that multiply together to make 93552 are 2 x 2 x 2 x 2 x 3 x 1949. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 93552 by the number (A) squared. 4 squared is 16 and 93552 divided by 16 is 5847. Therefore, B equals 5847.

Once again we have A and B and can get our answer to 93552 in its simplest radical form as follows:

√93552 = A√B

√93552 = 4√5847

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Simplify Square Root of 93553
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