Simplify Square Root of 37680

Here we will show you two methods that you can use to simplify the square root of 37680. In other words, we will show you how to find the square root of 37680 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.

√37680 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37680 to simplify the square root of 37680. 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 37680. The factors of 37680 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 157, 240, 314, 471, 628, 785, 942, 1256, 1570, 1884, 2355, 2512, 3140, 3768, 4710, 6280, 7536, 9420, 12560, 18840, and 37680. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 37680 divided by the greatest perfect square from the list of all factors of 37680. We determined above that the greatest perfect square from the list of all factors of 37680 is 16. Furthermore, 37680 divided by 16 is 2355, therefore B equals 2355.

Now we have A and B and can get our answer to 37680 in its simplest radical form as follows:

√37680 = A√B

√37680 = 4√2355

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37680 to simplify the square root of 37680 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 37680 and then take the square root of that product. The prime factors that multiply together to make 37680 are 2 x 2 x 2 x 2 x 3 x 5 x 157. 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 37680 by the number (A) squared. 4 squared is 16 and 37680 divided by 16 is 2355. Therefore, B equals 2355.

Once again we have A and B and can get our answer to 37680 in its simplest radical form as follows:

√37680 = A√B

√37680 = 4√2355

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