Simplify Square Root of 37404

Here we will show you two methods that you can use to simplify the square root of 37404. In other words, we will show you how to find the square root of 37404 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.

√37404 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37404 to simplify the square root of 37404. 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 37404. The factors of 37404 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 1039, 2078, 3117, 4156, 6234, 9351, 12468, 18702, and 37404. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 37404 divided by the greatest perfect square from the list of all factors of 37404. We determined above that the greatest perfect square from the list of all factors of 37404 is 36. Furthermore, 37404 divided by 36 is 1039, therefore B equals 1039.

Now we have A and B and can get our answer to 37404 in its simplest radical form as follows:

√37404 = A√B

√37404 = 6√1039

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37404 to simplify the square root of 37404 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 37404 and then take the square root of that product. The prime factors that multiply together to make 37404 are 2 x 2 x 3 x 3 x 1039. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 37404 by the number (A) squared. 6 squared is 36 and 37404 divided by 36 is 1039. Therefore, B equals 1039.

Once again we have A and B and can get our answer to 37404 in its simplest radical form as follows:

√37404 = A√B

√37404 = 6√1039

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Simplify Square Root of 37405
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